diff --git a/m4/openssl.m4 b/m4/openssl.m4
index e5cd3712..83f27be7 100644
--- a/m4/openssl.m4
+++ b/m4/openssl.m4
@@ -70,10 +70,10 @@ AC_DEFUN([_RRA_LIB_OPENSSL_INTERNAL],
         [AC_MSG_ERROR([cannot find usable OpenSSL crypto library])])],
     [$rra_openssl_extra])
  AS_IF([test x"$rra_reduced_depends" = xtrue],
-    [AC_CHECK_LIB([ssl], [SSL_library_init], [OPENSSL_LIBS=-lssl],
+    [AC_CHECK_LIB([ssl], [SSL_accept], [OPENSSL_LIBS=-lssl],
         [AS_IF([test x"$1" = xtrue],
             [AC_MSG_ERROR([cannot find usable OpenSSL library])])])],
-    [AC_CHECK_LIB([ssl], [SSL_library_init],
+    [AC_CHECK_LIB([ssl], [SSL_accept],
         [OPENSSL_LIBS="-lssl $CRYPTO_LIBS"],
         [AS_IF([test x"$1" = xtrue],
             [AC_MSG_ERROR([cannot find usable OpenSSL library])])],