diff --git a/elf/Makefile b/elf/Makefile
index 6702993..fc9c685 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -215,7 +215,7 @@ tests-internal += loadtest unload unload2 circleload1 \
tst-tls3 tst-tls6 tst-tls7 tst-tls8 tst-dlmopen2 \
tst-ptrguard1 tst-stackguard1 tst-libc_dlvsym \
tst-create_format1 tst-tls-surplus tst-dl-hwcaps_split
-tests-container += tst-pldd
+tests-container += tst-pldd tst-preload-pthread-libc
ifeq ($(build-hardcoded-path-in-tests),yes)
tests += tst-dlopen-aout
tst-dlopen-aout-no-pie = yes
diff --git a/elf/dl-deps.c b/elf/dl-deps.c
index 50f053a..007069f 100644
--- a/elf/dl-deps.c
+++ b/elf/dl-deps.c
@@ -610,7 +610,12 @@ Filters not supported with LD_TRACE_PRELINKING"));
memcpy (l_initfini, map->l_searchlist.r_list,
nlist * sizeof (struct link_map *));
- _dl_sort_maps (&l_initfini[1], nlist - 1, NULL, false);
+ /* If libc.so.6 is the main map, it participates in the sort, so
+ that the relocation order is correct regarding libc.so.6. */
+ if (l_initfini[0] == GL (dl_ns)[l_initfini[0]->l_ns].libc_map)
+ _dl_sort_maps (l_initfini, nlist, NULL, false);
+ else
+ _dl_sort_maps (&l_initfini[1], nlist - 1, NULL, false);
/* Terminate the list of dependencies. */
l_initfini[nlist] = NULL;
diff --git a/elf/tst-preload-pthread-libc.c b/elf/tst-preload-pthread-libc.c
new file mode 100644
index 0000000..48cb512
--- /dev/null
+++ b/elf/tst-preload-pthread-libc.c
@@ -0,0 +1,36 @@
+/* Test relocation ordering if the main executable is libc.so.6 (bug 20972).
+ Copyright (C) 2020 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ . */
+
+#include
+#include
+#include
+#include
+
+int
+main (void)
+{
+ char *libc = xasprintf ("%s/%s", support_slibdir_prefix, LIBC_SO);
+ char *argv[] = { libc, NULL };
+ char *envp[] = { (char *) "LD_PRELOAD=" LIBPTHREAD_SO,
+ /* Relocation ordering matters most without lazy binding. */
+ (char *) "LD_BIND_NOW=1",
+ NULL };
+ execve (libc, argv, envp);
+ printf ("execve of %s failed: %m\n", libc);
+ return 1;
+}