diff --git a/bisect.c b/bisect.c
index ec7487e683..ef5ee5a643 100644
--- a/bisect.c
+++ b/bisect.c
@@ -472,7 +472,6 @@ static GIT_PATH_FUNC(git_path_bisect_start, "BISECT_START")
 static GIT_PATH_FUNC(git_path_bisect_log, "BISECT_LOG")
 static GIT_PATH_FUNC(git_path_bisect_terms, "BISECT_TERMS")
 static GIT_PATH_FUNC(git_path_bisect_first_parent, "BISECT_FIRST_PARENT")
-static GIT_PATH_FUNC(git_path_head_name, "head-name")
 
 static void read_bisect_paths(struct strvec *array)
 {
@@ -1188,8 +1187,6 @@ int bisect_clean_state(void)
 	unlink_or_warn(git_path_bisect_run());
 	unlink_or_warn(git_path_bisect_terms());
 	unlink_or_warn(git_path_bisect_first_parent());
-	/* Cleanup head-name if it got left by an old version of git-bisect */
-	unlink_or_warn(git_path_head_name());
 	/*
 	 * Cleanup BISECT_START last to support the --no-checkout option
 	 * introduced in the commit 4796e823a.
diff --git a/t/t6030-bisect-porcelain.sh b/t/t6030-bisect-porcelain.sh
index 0a62ea2b3c..3ba4fdf615 100755
--- a/t/t6030-bisect-porcelain.sh
+++ b/t/t6030-bisect-porcelain.sh
@@ -1158,7 +1158,6 @@ test_expect_success 'git bisect reset cleans bisection state properly' '
 	test_path_is_missing ".git/BISECT_LOG" &&
 	test_path_is_missing ".git/BISECT_RUN" &&
 	test_path_is_missing ".git/BISECT_TERMS" &&
-	test_path_is_missing ".git/head-name" &&
 	test_path_is_missing ".git/BISECT_HEAD" &&
 	test_path_is_missing ".git/BISECT_START"
 '