diff --git a/lib/tempname.c b/lib/tempname.c
index e6520191d7..e3d09d963d 100644
--- a/lib/tempname.c
+++ b/lib/tempname.c
@@ -71,7 +71,8 @@
 
 /* Use getrandom if it works, falling back on a 64-bit linear
    congruential generator that starts with Var's value
-   mixed in with a clock's low-order bits if available.  */
+   mixed in with a clock's low-order bits (or with some other
+   pseudorandom number) if available.  */
 typedef uint_fast64_t random_value;
 #define RANDOM_VALUE_MAX UINT_FAST64_MAX
 #define BASE_62_DIGITS 10 /* 62**10 < UINT_FAST64_MAX */
@@ -89,6 +90,9 @@ random_bits (random_value var, bool use_getrandom)
   struct __timespec64 tv;
   __clock_gettime64 (CLOCK_MONOTONIC, &tv);
   var ^= tv.tv_nsec;
+#else
+  /* Fall back on pseudorandom number <https://bugs.gnu.org/57129>.  */
+  var ^= rand ();
 #endif
   return 2862933555777941757 * var + 3037000493;
 }