diff --git a/Doc/library/random.rst b/Doc/library/random.rst
index 291eca3a3f16a1..b75bd917229744 100644
--- a/Doc/library/random.rst
+++ b/Doc/library/random.rst
@@ -38,6 +38,8 @@ basic generator of your own devising: in that case, override the :meth:`~Random.
 :meth:`~Random.seed`, :meth:`~Random.getstate`, and :meth:`~Random.setstate` methods.
 Optionally, a new generator can supply a :meth:`~Random.getrandbits` method --- this
 allows :meth:`randrange` to produce selections over an arbitrarily large range.
+In subclasses, :meth:`randbytes` is implemented with the
+:meth:`~Random.getrandbits` method, unless :meth:`randbytes` is overriden.
 
 The :mod:`random` module also provides the :class:`SystemRandom` class which
 uses the system function :func:`os.urandom` to generate random numbers
diff --git a/Lib/random.py b/Lib/random.py
index f1df18d5c187b8..3ddff7cc446b18 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -120,6 +120,12 @@ def __init_subclass__(cls, /, **kwargs):
                 cls._randbelow = cls._randbelow_without_getrandbits
                 break
 
+        if (cls.randbytes == _random.Random.randbytes
+           and cls.getrandbits != _random.Random.getrandbits):
+            # Subclasses of random.Random implement randbytes()
+            # using getrandbits() if getrandbits() is overriden.
+            cls.randbytes = cls._randbytes_getrandbits
+
     def seed(self, a=None, version=2):
         """Initialize internal state from a seed.
 
@@ -189,6 +195,13 @@ def setstate(self, state):
                              "Random.setstate() of version %s" %
                              (version, self.VERSION))
 
+## -------------------- bytes -----------------------------
+
+    # Implementation used by Random and SystemRandom subclasses
+    def _randbytes_getrandbits (self, n):
+        """Generate n random bytes."""
+        return self.getrandbits(n * 8).to_bytes(n, 'little')
+
 ## ---- Methods below this point do not need to be overridden when
 ## ---- subclassing for the purpose of using a different core generator.
 
@@ -732,6 +745,15 @@ class SystemRandom(Random):
      Not available on all systems (see os.urandom() for details).
     """
 
+    def __init_subclass__(cls, /, **kwargs):
+        super().__init_subclass__(**kwargs)
+
+        if (cls.randbytes == SystemRandom.randbytes
+           and cls.getrandbits != SystemRandom.getrandbits):
+            # Subclasses of random.SystemRandom implement randbytes()
+            # using getrandbits() if getrandbits() is overriden.
+            cls.randbytes = cls._randbytes_getrandbits
+
     def random(self):
         """Get the next random number in the range [0.0, 1.0)."""
         return (int.from_bytes(_urandom(7), 'big') >> 3) * RECIP_BPF
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index 42c68dd1c24422..4785eb8f6b3ade 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -335,6 +335,65 @@ def test_randbytes(self):
         self.assertRaises(ValueError, self.gen.randbytes, -1)
         self.assertRaises(TypeError, self.gen.randbytes, 1.0)
 
+    def test_randbytes_subclass(self):
+        # For random.Random and random.SystemRandom subclasses,
+        # randbytes() is implemented with getrandbits()
+
+        # Subclass implements getrandbits() but not randbytes()
+        class Subclass(type(self.gen)):
+            def __init__(self):
+                super().__init__()
+                self.getrandbits_calls = []
+
+            def getrandbits(self, n):
+                self.getrandbits_calls.append(n)
+                return 0
+
+        subclass = Subclass()
+        for n in range(10):
+            self.assertEqual(subclass.randbytes(n), b'\0' * n)
+        self.assertEqual(subclass.getrandbits_calls,
+                         [n * 8 for n in range(10)])
+
+        # SubSubclass override explicitly randbytes():
+        # getrandbits() implemented in Subclass is not called.
+        class SubSubclass(Subclass):
+            def __init__(self):
+                super().__init__()
+                self.randbytes_calls = []
+
+            def randbytes(self, n):
+                self.randbytes_calls.append(n)
+                return b'\x04' * n
+
+        subsubclass = SubSubclass()
+        for n in range(10):
+            self.assertEqual(subsubclass.randbytes(n), b'\x04' * n)
+        self.assertEqual(subsubclass.randbytes_calls, list(range(10)))
+        self.assertEqual(subsubclass.getrandbits_calls, [])
+
+        # Subclass2 implements getrandbits() and randbytes():
+        # randbytes() doesn't use getrandbits().
+        class Subclass2(type(self.gen)):
+            def __init__(self):
+                super().__init__()
+                self.getrandbits_calls = []
+
+            def getrandbits(self, n):
+                self.getrandbits_calls.append(n)
+                return 0
+
+            randbytes_calls = []
+            def randbytes(self, n):
+                self.randbytes_calls.append(n)
+                return b'\x07' * n
+
+        subclass2 = Subclass2()
+        for n in range(10):
+            self.assertEqual(subclass2.randbytes(n), b'\x07' * n)
+        self.assertEqual(subclass2.randbytes_calls, list(range(10)))
+        self.assertEqual(subclass2.getrandbits_calls, [])
+
 
 try:
     random.SystemRandom().random()
diff --git a/Misc/NEWS.d/next/Library/2020-04-24-11-22-10.bpo-40346.viRmGr.rst b/Misc/NEWS.d/next/Library/2020-04-24-11-22-10.bpo-40346.viRmGr.rst
new file mode 100644
index 00000000000000..b323c1c4e87c61
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-04-24-11-22-10.bpo-40346.viRmGr.rst
@@ -0,0 +1,3 @@
+Subclasses of the :class:`random.Random` and :class:`random.SystemRandom`
+classes now get a ``randbytes()`` method implementation which uses the
+``getrandbits()`` method.