diff --git a/lisp/calendar/time-date.el b/lisp/calendar/time-date.el
index e96e2e7e2db..59e236ce3c5 100644
--- a/lisp/calendar/time-date.el
+++ b/lisp/calendar/time-date.el
@@ -352,9 +352,13 @@ format-seconds
           ;; Cf article-make-date-line in gnus-art.
           (setq num (floor seconds unit)
                 seconds (- seconds (* num unit)))
-          (let ((is-zero (zerop (if (= unit 1)
-                                    (+ num fraction)
-                                  num))))
+          (let ((is-zero (if (and (zerop seconds) (= unit 1))
+                             ;; Also drop leading units when SECONDS is
+                             ;; 0 (bug#70322).
+                             nil
+                           (zerop (if (= unit 1)
+                                      (+ num fraction)
+                                    num)))))
             ;; Start position of the first non-zero unit.
             (when (and (not leading-zeropos)
                        (not is-zero))