diff --git a/icu4c/source/i18n/rbt.cpp b/icu4c/source/i18n/rbt.cpp
index 0c198039be..6823882649 100644
--- a/icu4c/source/i18n/rbt.cpp
+++ b/icu4c/source/i18n/rbt.cpp
@@ -91,9 +91,26 @@ RuleBasedTransliterator::handleTransliterate(Replaceable& text, Position& index,
     int32_t limit = index.limit;
     int32_t cursor = index.cursor;
 
+    /* A rule like
+     *   a>b|a
+     * creates an infinite loop. To prevent that, we put an arbitrary
+     * limit on the number of iterations that we take, one that is
+     * high enough that any reasonable rules are ok, but low enough to
+     * prevent a server from hanging.  The limit is 16 times the
+     * number of characters n, unless n is so large that 16n exceeds a
+     * uint32_t.
+     */
+    uint32_t loopCount = 0;
+    uint32_t loopLimit = limit - cursor;
+    if (loopLimit >= 0x10000000) {
+        loopLimit = 0xFFFFFFFF;
+    } else {
+        loopLimit <<= 4;
+    }
+
     bool_t isPartial = FALSE;
 
-    while (cursor < limit) {
+    while (cursor < limit && loopCount <= loopLimit) {
         TransliterationRule* r = isIncremental ?
             data->ruleSet.findIncrementalMatch(text, start, limit, cursor,
                                                *data, isPartial,
@@ -121,6 +138,7 @@ RuleBasedTransliterator::handleTransliterate(Replaceable& text, Position& index,
                                       r->getOutput());
             limit += r->getOutput().length() - r->getKeyLength();
             cursor += r->getCursorPos();
+            ++loopCount;
         }
     }