diff --git a/icu4c/source/common/unorm.cpp b/icu4c/source/common/unorm.cpp
index 98387308b6..7cd1f42807 100644
--- a/icu4c/source/common/unorm.cpp
+++ b/icu4c/source/common/unorm.cpp
@@ -4494,4 +4494,123 @@ cleanup:
     return result;
 }
 
+/* data swapping ------------------------------------------------------------ */
+
+U_CAPI int32_t U_EXPORT2
+unorm_swap(const UDataSwapper *ds,
+           const void *inData, int32_t length, void *outData,
+           UErrorCode *pErrorCode) {
+    const UDataInfo *pInfo;
+    int32_t headerSize;
+
+    const uint8_t *inBytes;
+    uint8_t *outBytes;
+
+    const int32_t *inIndexes;
+    int32_t indexes[32];
+
+    int32_t i, offset, count, size;
+
+    /* udata_swapDataHeader checks the arguments */
+    headerSize=udata_swapDataHeader(ds, inData, length, outData, pErrorCode);
+    if(pErrorCode==NULL || U_FAILURE(*pErrorCode)) {
+        return 0;
+    }
+
+    /* check data format and format version */
+    pInfo=(const UDataInfo *)((const char *)inData+4);
+    if(!(
+        pInfo->dataFormat[0]==0x4e &&   /* dataFormat="Norm" */
+        pInfo->dataFormat[1]==0x6f &&
+        pInfo->dataFormat[2]==0x72 &&
+        pInfo->dataFormat[3]==0x6d &&
+        pInfo->formatVersion[0]==2
+    )) {
+        udata_printError(ds, "unorm_swap(): data format %02x.%02x.%02x.%02x (format version %02x) is not recognized as unorm.icu\n",
+                         pInfo->dataFormat[0], pInfo->dataFormat[1],
+                         pInfo->dataFormat[2], pInfo->dataFormat[3],
+                         pInfo->formatVersion[0]);
+        *pErrorCode=U_UNSUPPORTED_ERROR;
+        return 0;
+    }
+
+    inBytes=(const uint8_t *)inData+headerSize;
+    outBytes=(uint8_t *)outData+headerSize;
+
+    inIndexes=(const int32_t *)inBytes;
+
+    if(length>=0) {
+        length-=headerSize;
+        if(length<32*4) {
+            udata_printError(ds, "unorm_swap(): too few bytes (%d after header) for unorm.icu\n",
+                             length);
+            *pErrorCode=U_INDEX_OUTOFBOUNDS_ERROR;
+            return 0;
+        }
+    }
+
+    /* read the first 32 indexes (ICU 2.8/format version 2.2: _NORM_INDEX_TOP==32, might grow) */
+    for(i=0; i<32; ++i) {
+        indexes[i]=udata_readInt32(ds, inIndexes[i]);
+    }
+
+    /* calculate the total length of the data */
+    size=
+        32*4+ /* size of indexes[] */
+        indexes[_NORM_INDEX_TRIE_SIZE]+
+        indexes[_NORM_INDEX_UCHAR_COUNT]*2+
+        indexes[_NORM_INDEX_COMBINE_DATA_COUNT]*2+
+        indexes[_NORM_INDEX_FCD_TRIE_SIZE]+
+        indexes[_NORM_INDEX_AUX_TRIE_SIZE]+
+        indexes[_NORM_INDEX_CANON_SET_COUNT]*2;
+
+    if(length>=0) {
+        if(length<size) {
+            udata_printError(ds, "unorm_swap(): too few bytes (%d after header) for all of unorm.icu\n",
+                             length);
+            *pErrorCode=U_INDEX_OUTOFBOUNDS_ERROR;
+            return 0;
+        }
+
+        /* copy the data for inaccessible bytes */
+        if(inBytes!=outBytes) {
+            uprv_memcpy(outBytes, inBytes, size);
+        }
+
+        offset=0;
+
+        /* swap the indexes[] */
+        count=32*4;
+        ds->swapArray32(ds, inBytes, count, outBytes, pErrorCode);
+        offset+=count;
+
+        /* swap the main UTrie */
+        count=indexes[_NORM_INDEX_TRIE_SIZE];
+        utrie_swap(ds, inBytes+offset, count, outBytes+offset, pErrorCode);
+        offset+=count;
+
+        /* swap the uint16_t extraData[] and the uint16_t combiningTable[] */
+        count=(indexes[_NORM_INDEX_UCHAR_COUNT]+indexes[_NORM_INDEX_COMBINE_DATA_COUNT])*2;
+        ds->swapArray16(ds, inBytes+offset, count, outBytes+offset, pErrorCode);
+        offset+=count;
+
+        /* swap the FCD UTrie */
+        count=indexes[_NORM_INDEX_FCD_TRIE_SIZE];
+        utrie_swap(ds, inBytes+offset, count, outBytes+offset, pErrorCode);
+        offset+=count;
+
+        /* swap the aux UTrie */
+        count=indexes[_NORM_INDEX_AUX_TRIE_SIZE];
+        ds->swapArray32(ds, inBytes+offset, count, outBytes+offset, pErrorCode);
+        offset+=count;
+
+        /* swap the uint16_t combiningTable[] */
+        count=indexes[_NORM_INDEX_CANON_SET_COUNT]*2;
+        ds->swapArray16(ds, inBytes+offset, count, outBytes+offset, pErrorCode);
+        offset+=count;
+    }
+
+    return headerSize+size;
+}
+
 #endif /* #if !UCONFIG_NO_NORMALIZATION */
diff --git a/icu4c/source/common/unormimp.h b/icu4c/source/common/unormimp.h
index 284bca59e1..e3fe602c24 100644
--- a/icu4c/source/common/unormimp.h
+++ b/icu4c/source/common/unormimp.h
@@ -372,6 +372,15 @@ unorm_isNFSkippable(UChar32 c, UNormalizationMode mode);
 U_CAPI void U_EXPORT2
 unorm_addPropertyStarts(USet *set, UErrorCode *pErrorCode);
 
+/**
+ * Swap unorm.icu. See udataswp.h.
+ * @internal
+ */
+U_CAPI int32_t U_EXPORT2
+unorm_swap(const UDataSwapper *ds,
+           const void *inData, int32_t length, void *outData,
+           UErrorCode *pErrorCode);
+
 /**
  * Description of the format of unorm.dat version 2.2.
  *
@@ -391,7 +400,7 @@ unorm_addPropertyStarts(USet *set, UErrorCode *pErrorCode);
  * unorm.dat customarily begins with a UDataInfo structure, see udata.h and .c.
  * After that there are the following structures:
  *
- * uint16_t indexes[_NORM_INDEX_TOP];           -- _NORM_INDEX_TOP=32, see enum in this file
+ * int32_t indexes[_NORM_INDEX_TOP];            -- _NORM_INDEX_TOP=32, see enum in this file
  *
  * UTrie normTrie;                              -- size in bytes=indexes[_NORM_INDEX_TRIE_SIZE]
  * 
diff --git a/icu4c/source/tools/icuswap/icuswap.cpp b/icu4c/source/tools/icuswap/icuswap.cpp
index 59f8de759b..9ac20760ab 100644
--- a/icu4c/source/tools/icuswap/icuswap.cpp
+++ b/icu4c/source/tools/icuswap/icuswap.cpp
@@ -41,6 +41,7 @@
 #include "uprops.h"
 #include "ucol_swp.h"
 #include "ucnv_bld.h"
+#include "unormimp.h"
 
 /* swapping implementations in i18n */
 
@@ -285,6 +286,9 @@ static const struct {
     { { 0x43, 0x6d, 0x6e, 0x44 }, udata_swapPackage },  /* dataFormat="CmnD" */
     /* insert data formats here, descending by expected frequency of occurrence */
     { { 0x55, 0x50, 0x72, 0x6f }, uprops_swap },        /* dataFormat="UPro" */
+#if !UCONFIG_NO_NORMALIZATION
+    { { 0x4e, 0x6f, 0x72, 0x6d }, unorm_swap },         /* dataFormat="Norm" */
+#endif
 #if !UCONFIG_NO_COLLATION
     { { 0x55, 0x43, 0x6f, 0x6c }, ucol_swap },          /* dataFormat="UCol" */
     { { 0x49, 0x6e, 0x76, 0x43 }, ucol_swapInverseUCA },/* dataFormat="InvC" */