diff --git a/test/units/testsuite-01.service b/test/units/testsuite-01.service
index a55cc526a5..9074e0968f 100644
--- a/test/units/testsuite-01.service
+++ b/test/units/testsuite-01.service
@@ -1,10 +1,7 @@
 # SPDX-License-Identifier: LGPL-2.1-or-later
 [Unit]
 Description=TEST-01-BASIC
-# Order the test unit after systemd-update-utmp-runlevel.service, since
-# the service doesn't play well with daemon-reexec
-# See: https://github.com/systemd/systemd/issues/27167
-After=multi-user.target systemd-update-utmp-runlevel.service
+After=multi-user.target
 Wants=systemd-resolved.service systemd-networkd.service
 
 [Service]