diff --git a/mysql-test/r/subselect.result b/mysql-test/r/subselect.result
index 6094d23b0d0..33b12c05f98 100644
--- a/mysql-test/r/subselect.result
+++ b/mysql-test/r/subselect.result
@@ -3131,3 +3131,29 @@ a	sum
 3	20
 4	40
 DROP TABLE t1,t2,t3;
+CREATE TABLE t1 (a varchar(5), b varchar(10));
+INSERT INTO t1 VALUES
+('AAA', 5), ('BBB', 4), ('BBB', 1), ('CCC', 2),
+('CCC', 7), ('AAA', 2), ('AAA', 4), ('BBB', 3), ('AAA', 8);
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+a	b
+BBB	4
+CCC	7
+AAA	8
+EXPLAIN
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	PRIMARY	t1	ALL	NULL	NULL	NULL	NULL	9	Using where
+2	DEPENDENT SUBQUERY	t1	ALL	NULL	NULL	NULL	NULL	9	Using temporary; Using filesort
+ALTER TABLE t1 ADD INDEX(a);
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+a	b
+BBB	4
+CCC	7
+AAA	8
+EXPLAIN
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
+1	PRIMARY	t1	ALL	NULL	NULL	NULL	NULL	9	Using where
+2	DEPENDENT SUBQUERY	t1	index	NULL	a	8	NULL	9	Using filesort
+DROP TABLE t1;
diff --git a/mysql-test/t/subselect.test b/mysql-test/t/subselect.test
index 762ff36ba63..9e09b215951 100644
--- a/mysql-test/t/subselect.test
+++ b/mysql-test/t/subselect.test
@@ -2051,3 +2051,25 @@ SELECT t1.a, SUM(b) AS sum  FROM t1 GROUP BY t1.a
                     HAVING t2.c+sum > 20);
 
 DROP TABLE t1,t2,t3;
+
+#
+# Test for bug #16603: GROUP BY in a row subquery with a quantifier 
+#                      when an index is defined on the grouping field
+
+CREATE TABLE t1 (a varchar(5), b varchar(10));
+INSERT INTO t1 VALUES
+  ('AAA', 5), ('BBB', 4), ('BBB', 1), ('CCC', 2),
+  ('CCC', 7), ('AAA', 2), ('AAA', 4), ('BBB', 3), ('AAA', 8);
+
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+EXPLAIN
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+
+ALTER TABLE t1 ADD INDEX(a);
+
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+EXPLAIN
+SELECT * FROM t1 WHERE (a,b) = ANY (SELECT a, max(b) FROM t1 GROUP BY a);
+
+DROP TABLE t1;
+
diff --git a/sql/sql_select.cc b/sql/sql_select.cc
index 807cb129aca..768ae7bf71f 100644
--- a/sql/sql_select.cc
+++ b/sql/sql_select.cc
@@ -364,22 +364,8 @@ JOIN::prepare(Item ***rref_pointer_array,
     select_lex->having_fix_field= 0;
     if (having_fix_rc || thd->net.report_error)
       DBUG_RETURN(-1);				/* purecov: inspected */
-    if (having->with_sum_func)
-      having->split_sum_func2(thd, ref_pointer_array, all_fields,
-                              &having, TRUE);
     thd->lex->allow_sum_func= save_allow_sum_func;
   }
-  if (select_lex->inner_sum_func_list)
-  {
-    Item_sum *end=select_lex->inner_sum_func_list;
-    Item_sum *item_sum= end;  
-    do
-    { 
-      item_sum= item_sum->next;
-      item_sum->split_sum_func2(thd, ref_pointer_array,
-                                all_fields, item_sum->ref_by, FALSE);
-    } while (item_sum != end);
-  }
 
   if (!thd->lex->view_prepare_mode)
   {
@@ -397,6 +383,21 @@ JOIN::prepare(Item ***rref_pointer_array,
     }
   }
 
+  if (having && having->with_sum_func)
+    having->split_sum_func2(thd, ref_pointer_array, all_fields,
+                            &having, TRUE);
+  if (select_lex->inner_sum_func_list)
+  {
+    Item_sum *end=select_lex->inner_sum_func_list;
+    Item_sum *item_sum= end;  
+    do
+    { 
+      item_sum= item_sum->next;
+      item_sum->split_sum_func2(thd, ref_pointer_array,
+                                all_fields, item_sum->ref_by, FALSE);
+    } while (item_sum != end);
+  }
+
   if (setup_ftfuncs(select_lex)) /* should be after having->fix_fields */
     DBUG_RETURN(-1);