diff --git a/mysql-test/r/select.result b/mysql-test/r/select.result
index f8df72c6709..5453345d50c 100644
--- a/mysql-test/r/select.result
+++ b/mysql-test/r/select.result
@@ -4875,4 +4875,31 @@ f1	f1	f1	f1	f2	f1	f1
 18	9	NULL	NULL	NULL	5	7
 SET SESSION join_buffer_size = DEFAULT;
 DROP TABLE t1,t2,t3,t4,t5,t6;
+CREATE TABLE t1(f1 int UNSIGNED) engine=myisam;
+INSERT INTO t1 VALUES (3),(2),(1);
+set sql_buffer_result=0;
+SELECT f1 FROM t1 GROUP BY 1;
+f1
+1
+2
+3
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+f1
+3
+SELECT 1 FROM t1 GROUP BY 1;
+1
+1
+set sql_buffer_result=1;
+SELECT f1 FROM t1 GROUP BY 1;
+f1
+1
+2
+3
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+f1
+3
+SELECT 1 FROM t1 GROUP BY 1;
+1
+1
+drop table t1;
 End of 5.1 tests
diff --git a/mysql-test/r/select_pkeycache.result b/mysql-test/r/select_pkeycache.result
index f8df72c6709..5453345d50c 100644
--- a/mysql-test/r/select_pkeycache.result
+++ b/mysql-test/r/select_pkeycache.result
@@ -4875,4 +4875,31 @@ f1	f1	f1	f1	f2	f1	f1
 18	9	NULL	NULL	NULL	5	7
 SET SESSION join_buffer_size = DEFAULT;
 DROP TABLE t1,t2,t3,t4,t5,t6;
+CREATE TABLE t1(f1 int UNSIGNED) engine=myisam;
+INSERT INTO t1 VALUES (3),(2),(1);
+set sql_buffer_result=0;
+SELECT f1 FROM t1 GROUP BY 1;
+f1
+1
+2
+3
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+f1
+3
+SELECT 1 FROM t1 GROUP BY 1;
+1
+1
+set sql_buffer_result=1;
+SELECT f1 FROM t1 GROUP BY 1;
+f1
+1
+2
+3
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+f1
+3
+SELECT 1 FROM t1 GROUP BY 1;
+1
+1
+drop table t1;
 End of 5.1 tests
diff --git a/mysql-test/t/select.test b/mysql-test/t/select.test
index 1139e7acc60..ef1894a5405 100644
--- a/mysql-test/t/select.test
+++ b/mysql-test/t/select.test
@@ -4121,4 +4121,21 @@ SET SESSION join_buffer_size = DEFAULT;
 
 DROP TABLE t1,t2,t3,t4,t5,t6;
 
+#
+# Bug #780425: "sql_buffer_result=1 gives wrong result for GROUP BY with a
+# constant expression"
+#
+
+CREATE TABLE t1(f1 int UNSIGNED) engine=myisam;
+INSERT INTO t1 VALUES (3),(2),(1);
+set sql_buffer_result=0;
+SELECT f1 FROM t1 GROUP BY 1;
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+SELECT 1 FROM t1 GROUP BY 1;
+set sql_buffer_result=1;
+SELECT f1 FROM t1 GROUP BY 1;
+SELECT f1 FROM t1 GROUP BY '123' = 'abc';
+SELECT 1 FROM t1 GROUP BY 1;
+drop table t1;
+
 --echo End of 5.1 tests
diff --git a/sql/sql_select.cc b/sql/sql_select.cc
index defd7ed7c32..d1fcb5633bb 100644
--- a/sql/sql_select.cc
+++ b/sql/sql_select.cc
@@ -1295,7 +1295,10 @@ JOIN::optimize()
       DBUG_RETURN(1);
     }
     if (old_group_list && !group_list)
+    {
+      DBUG_ASSERT(group);
       select_distinct= 0;
+    }
   }
   if (!group_list && group)
   {
@@ -1303,6 +1306,7 @@ JOIN::optimize()
     simple_order=1;
     select_distinct= 0;                       // No need in distinct for 1 row
     group_optimized_away= 1;
+    implicit_grouping= TRUE;
   }
 
   calc_group_buffer(this, group_list);