diff --git a/elf/Makefile b/elf/Makefile
index 9b09f09e3c..6c62ed611c 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -200,7 +200,8 @@ tests += restest1 preloadtest loadfail multiload origtest resolvfail \
 	 tst-debug1 tst-main1 tst-absolute-sym tst-absolute-zero tst-big-note \
 	 tst-unwind-ctor tst-unwind-main tst-audit13 \
 	 tst-sonamemove-link tst-sonamemove-dlopen tst-dlopen-tlsmodid \
-	 tst-dlopen-self tst-auditmany tst-initfinilazyfail tst-dlopenfail
+	 tst-dlopen-self tst-auditmany tst-initfinilazyfail tst-dlopenfail \
+	 tst-dlopenfail-2
 #	 reldep9
 tests-internal += loadtest unload unload2 circleload1 \
 	 neededtest neededtest2 neededtest3 neededtest4 \
@@ -311,7 +312,7 @@ modules-names = testobj1 testobj2 testobj3 testobj4 testobj5 testobj6 \
 		tst-auditmanymod7 tst-auditmanymod8 tst-auditmanymod9 \
 		tst-initlazyfailmod tst-finilazyfailmod \
 		tst-dlopenfailmod1 tst-dlopenfaillinkmod tst-dlopenfailmod2 \
-		tst-ldconfig-ld-mod
+		tst-dlopenfailmod3 tst-ldconfig-ld-mod
 # Most modules build with _ISOMAC defined, but those filtered out
 # depend on internal headers.
 modules-names-tests = $(filter-out ifuncmod% tst-libc_dlvsym-dso tst-tlsmod%,\
@@ -1645,6 +1646,10 @@ $(objpfx)tst-dlopenfailmod1.so: \
   $(shared-thread-library) $(objpfx)tst-dlopenfaillinkmod.so
 LDFLAGS-tst-dlopenfaillinkmod.so = -Wl,-soname,tst-dlopenfail-missingmod.so
 $(objpfx)tst-dlopenfailmod2.so: $(shared-thread-library)
+$(objpfx)tst-dlopenfail-2: $(libdl)
+$(objpfx)tst-dlopenfail.out: \
+  $(objpfx)tst-dlopenfailmod1.so $(objpfx)tst-dlopenfailmod2.so \
+  $(objpfx)tst-dlopenfailmod3.so
 
 $(objpfx)tst-dlopen-nodelete-reloc: $(libdl)
 $(objpfx)tst-dlopen-nodelete-reloc.out: \
diff --git a/elf/tst-dlopenfail-2.c b/elf/tst-dlopenfail-2.c
new file mode 100644
index 0000000000..35bbde64ab
--- /dev/null
+++ b/elf/tst-dlopenfail-2.c
@@ -0,0 +1,59 @@
+/* Test unrelated dlopen after dlopen failure involving NODELETE.
+   Copyright (C) 2019-2020 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
+   <https://www.gnu.org/licenses/>.  */
+
+#include <dlfcn.h>
+#include <errno.h>
+#include <gnu/lib-names.h>
+#include <stddef.h>
+#include <stdio.h>
+#include <string.h>
+#include <support/check.h>
+#include <support/xdlfcn.h>
+
+static int
+do_test (void)
+{
+  /* This test uses libpthread as the canonical NODELETE module.  If
+     libpthread is no longer NODELETE because it has been merged into
+     libc, the test needs to be updated.  */
+  TEST_VERIFY (dlsym (NULL, "pthread_create") == NULL);
+
+  /* This is expected to fail because of the missing dependency.  */
+  puts ("info: attempting to load tst-dlopenfailmod1.so");
+  TEST_VERIFY (dlopen ("tst-dlopenfailmod1.so", RTLD_LAZY) == NULL);
+  const char *message = dlerror ();
+  TEST_COMPARE_STRING (message,
+                       "tst-dlopenfail-missingmod.so:"
+                       " cannot open shared object file:"
+                       " No such file or directory");
+
+  /* Open a small shared object.  With a dangling GL (dl_initfirst)
+     pointer, this is likely to crash because there is no longer any
+     mapped text segment there (bug 25396).  */
+
+  puts ("info: attempting to load tst-dlopenfailmod3.so");
+  xdlclose (xdlopen ("tst-dlopenfailmod3.so", RTLD_NOW));
+
+  return 0;
+}
+
+/* Do not perturb the dangling link map.  With M_PERTURB, the link map
+   appears to have l_init_called set, so there are no constructor
+   calls and no crashes.  */
+#define TEST_NO_MALLOPT
+#include <support/test-driver.c>
diff --git a/elf/tst-dlopenfailmod3.c b/elf/tst-dlopenfailmod3.c
new file mode 100644
index 0000000000..636e971264
--- /dev/null
+++ b/elf/tst-dlopenfailmod3.c
@@ -0,0 +1,17 @@
+/* Empty module for the tst-dlopenfail-2 test.
+   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
+   <https://www.gnu.org/licenses/>.  */
