diff --git a/src/pkg/bytes/bytes.go b/src/pkg/bytes/bytes.go
index 644bf75b894..0c53e4c0b71 100644
--- a/src/pkg/bytes/bytes.go
+++ b/src/pkg/bytes/bytes.go
@@ -356,7 +356,11 @@ func Map(mapping func(r rune) rune, s []byte) []byte {
 		}
 		r = mapping(r)
 		if r >= 0 {
-			if nbytes+utf8.RuneLen(r) > maxbytes {
+			rl := utf8.RuneLen(r)
+			if rl < 0 {
+				rl = len(string(utf8.RuneError))
+			}
+			if nbytes+rl > maxbytes {
 				// Grow the buffer.
 				maxbytes = maxbytes*2 + utf8.UTFMax
 				nb := make([]byte, maxbytes)
diff --git a/src/pkg/bytes/bytes_test.go b/src/pkg/bytes/bytes_test.go
index 808655a4a48..b16ac9f515c 100644
--- a/src/pkg/bytes/bytes_test.go
+++ b/src/pkg/bytes/bytes_test.go
@@ -785,6 +785,16 @@ func TestMap(t *testing.T) {
 	if string(m) != expect {
 		t.Errorf("drop: expected %q got %q", expect, m)
 	}
+
+	// 6. Invalid rune
+	invalidRune := func(r rune) rune {
+		return utf8.MaxRune + 1
+	}
+	m = Map(invalidRune, []byte("x"))
+	expect = "\uFFFD"
+	if string(m) != expect {
+		t.Errorf("invalidRune: expected %q got %q", expect, m)
+	}
 }
 
 func TestToUpper(t *testing.T) { runStringTests(t, ToUpper, "ToUpper", upperTests) }