diff --git a/setup.c b/setup.c
index 4a15b10..20a1f0f 100644
--- a/setup.c
+++ b/setup.c
@@ -721,8 +721,10 @@ static const char *setup_discovered_git_dir(const char *gitdir,
 	if (offset == cwd->len)
 		return NULL;
 
-	/* Make "offset" point to past the '/', and add a '/' at the end */
-	offset++;
+	/* Make "offset" point past the '/' (already the case for root dirs) */
+	if (offset != offset_1st_component(cwd->buf))
+		offset++;
+	/* Add a '/' at the end */
 	strbuf_addch(cwd, '/');
 	return cwd->buf + offset;
 }