diff --git a/git-bisect.sh b/git-bisect.sh
index 5385249890..393fa35584 100755
--- a/git-bisect.sh
+++ b/git-bisect.sh
@@ -26,6 +26,9 @@ OPTIONS_SPEC=
 . git-sh-setup
 require_work_tree
 
+_x40='[0-9a-f][0-9a-f][0-9a-f][0-9a-f][0-9a-f]'
+_x40="$_x40$_x40$_x40$_x40$_x40$_x40$_x40$_x40"
+
 sq() {
 	@@PERL@@ -e '
 		for (@ARGV) {
@@ -60,7 +63,8 @@ bisect_start() {
 	# top-of-line master first!
 	#
 	head=$(GIT_DIR="$GIT_DIR" git symbolic-ref HEAD) ||
-	die "Bad HEAD - I need a symbolic ref"
+	head=$(GIT_DIR="$GIT_DIR" git rev-parse --verify HEAD) ||
+	die "Bad HEAD - I need a HEAD"
 	case "$head" in
 	refs/heads/bisect)
 		if [ -s "$GIT_DIR/head-name" ]; then
@@ -70,7 +74,7 @@ bisect_start() {
 		fi
 		git checkout $branch || exit
 		;;
-	refs/heads/*)
+	refs/heads/*|$_x40)
 		[ -s "$GIT_DIR/head-name" ] && die "won't bisect on seeked tree"
 		echo "${head#refs/heads/}" >"$GIT_DIR/head-name"
 		;;
diff --git a/t/t6030-bisect-porcelain.sh b/t/t6030-bisect-porcelain.sh
index 2ba4b00e52..ec71123f4b 100755
--- a/t/t6030-bisect-porcelain.sh
+++ b/t/t6030-bisect-porcelain.sh
@@ -254,6 +254,18 @@ test_expect_success 'bisect run & skip: find first bad' '
 	grep "$HASH6 is first bad commit" my_bisect_log.txt
 '
 
+test_expect_success 'bisect starting with a detached HEAD' '
+
+	git bisect reset &&
+	git checkout master^ &&
+	HEAD=$(git rev-parse --verify HEAD) &&
+	git bisect start &&
+	test $HEAD = $(cat .git/head-name) &&
+	git bisect reset &&
+	test $HEAD = $(git rev-parse --verify HEAD)
+
+'
+
 #
 #
 test_done