diff --git a/datafusion/expr/src/udaf.rs b/datafusion/expr/src/udaf.rs
index 2243682cfd021..e97823f41bddd 100644
--- a/datafusion/expr/src/udaf.rs
+++ b/datafusion/expr/src/udaf.rs
@@ -792,7 +792,7 @@ pub fn udaf_default_schema_name<F: AggregateUDFImpl + ?Sized>(
 
     // exclude the first function argument(= column) in ordered set aggregate function,
     // because it is duplicated with the WITHIN GROUP clause in schema name.
-    let args = if func.is_ordered_set_aggregate() {
+    let args = if func.is_ordered_set_aggregate() && !order_by.is_empty() {
         &args[1..]
     } else {
         &args[..]
diff --git a/datafusion/sqllogictest/test_files/aggregate.slt b/datafusion/sqllogictest/test_files/aggregate.slt
index 332b35b6ad2e5..e6d2197076a27 100644
--- a/datafusion/sqllogictest/test_files/aggregate.slt
+++ b/datafusion/sqllogictest/test_files/aggregate.slt
@@ -1821,6 +1821,29 @@ c 122
 d 124
 e 115
 
+
+# using approx_percentile_cont on 2 columns with same signature
+query TII
+SELECT c1, approx_percentile_cont(c2, 0.95) AS c2, approx_percentile_cont(c3, 0.95) AS c3 FROM aggregate_test_100 GROUP BY 1 ORDER BY 1
+----
+a 5 73
+b 5 68
+c 5 122
+d 5 124
+e 5 115
+
+# error is unique to this UDAF
+query TRR
+SELECT c1, avg(c2) AS c2, avg(c3) AS c3 FROM aggregate_test_100 GROUP BY 1 ORDER BY 1
+----
+a 2.857142857143 -18.333333333333
+b 3.263157894737 -5.842105263158
+c 2.666666666667 -1.333333333333
+d 2.444444444444 25.444444444444
+e 3 40.333333333333
+
+
+
 query TI
 SELECT c1, approx_percentile_cont(0.95) WITHIN GROUP (ORDER BY c3 DESC) AS c3_p95 FROM aggregate_test_100 GROUP BY 1 ORDER BY 1
 ----