diff --git a/refs.c b/refs.c
index e3c05110e58ca5684f9c43b1e1a5eb2587c96828..6f471d42c37ab4e66f402d1c983d3d42e4ebb2d8 100644
--- a/refs.c
+++ b/refs.c
@@ -837,7 +837,7 @@ int for_each_rawref(each_ref_fn fn, void *cb_data)
 
 static inline int bad_ref_char(int ch)
 {
-	if (((unsigned) ch) <= ' ' ||
+	if (((unsigned) ch) <= ' ' || ch == 0x7f ||
 	    ch == '~' || ch == '^' || ch == ':' || ch == '\\')
 		return 1;
 	/* 2.13 Pattern Matching Notation */
diff --git a/t/t1402-check-ref-format.sh b/t/t1402-check-ref-format.sh
index 7563043c53f09cd28b77bcc4f227ecf3a855f163..ed4275afe3100491ea57025632665182127f33cf 100755
--- a/t/t1402-check-ref-format.sh
+++ b/t/t1402-check-ref-format.sh
@@ -30,6 +30,9 @@ invalid_ref 'heads/foo.lock'
 valid_ref 'heads/foo@bar'
 invalid_ref 'heads/v@{ation'
 invalid_ref 'heads/foo\bar'
+invalid_ref "$(printf 'heads/foo\t')"
+invalid_ref "$(printf 'heads/foo\177')"
+valid_ref "$(printf 'heads/fu\303\237')"
 
 test_expect_success "check-ref-format --branch @{-1}" '
 	T=$(git write-tree) &&