diff --git a/icu4c/source/stubdata/Makefile.in b/icu4c/source/stubdata/Makefile.in
index af94d5c6c00..a0fc581f129 100644
--- a/icu4c/source/stubdata/Makefile.in
+++ b/icu4c/source/stubdata/Makefile.in
@@ -94,8 +94,11 @@ ifneq ($(ENABLE_STATIC),)
 	$(INSTALL-L) $(TARGET) $(DESTDIR)$(libdir)/$(TARGET)
 endif
 ifneq ($(ENABLE_SHARED),)
-	$(INSTALL-L) $(MIDDLE_SO_TARGET) $(DESTDIR)$(libdir)/$(MIDDLE_SO_TARGET)
-	cd $(DESTDIR)$(libdir) && $(RM) $(SO_TARGET) && ln -s $(MIDDLE_SO_TARGET) $(SO_TARGET)
+	$(INSTALL-L) $(FINAL_SO_TARGET) $(DESTDIR)$(libdir)/$(FINAL_SO_TARGET)
+ifneq ($(FINAL_SO_TARGET),$(SO_TARGET))
+	cd $(DESTDIR)$(libdir) && $(RM) $(MIDDLE_SO_TARGET) && ln -s $(FINAL_SO_TARGET) $(MIDDLE_SO_TARGET)
+	cd $(DESTDIR)$(libdir) && $(RM) $(SO_TARGET) && ln -s $(FINAL_SO_TARGET) $(SO_TARGET)
+endif
 endif
 
 dist-local: