diff --git a/optax/contrib/_scale_by_grad_norm.py b/optax/contrib/_scale_by_grad_norm.py
new file mode 100644
index 00000000..8e775f79
--- /dev/null
+++ b/optax/contrib/_scale_by_grad_norm.py
@@ -0,0 +1,61 @@
+# Copyright 2023 DeepMind Technologies Limited. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""GradientTransformation to scale by the gradient norm"""
+
+import jax
+
+from optax._src import base
+from optax._src import utils
+
+from typing import NamedTuple
+
+
+class ScaleByGradientNorm(NamedTuple):
+  """State of `GradientTransformation` returned by `scale_by_gradient_norm`.
+
+  Attributes:
+    scale: (float) scaling factor
+    eps: (float) jitter term to avoid dividing by 0
+  """
+
+  scale: float
+  eps: float
+
+
+def scale_by_gradient_norm(
+  scale: float = 1.0, eps: float = 1e-6
+) -> base.GradientTransformation:
+  """
+  Scale by the norm of the gradient.
+
+  Args:
+    scale: (float) scaling factor
+    eps: (float) jitter term to avoid dividing by 0
+
+  Returns:
+    An (init_fn, update_fn) tuple.
+  """
+
+  def init_fn(params):
+    del params
+    return ScaleByGradientNorm(scale, eps)
+
+  def update_fn(updates, state, params=None):
+    del params
+    g_norm = (utils.global_norm(updates) + eps) / scale
+    updates = jax.tree_util.tree_map(lambda g: g / g_norm, updates)
+    return updates, state
+
+  return base.GradientTransformation(init_fn, update_fn)
diff --git a/optax/contrib/_scale_by_grad_norm_test.py b/optax/contrib/_scale_by_grad_norm_test.py
new file mode 100644
index 00000000..fd40a366
--- /dev/null
+++ b/optax/contrib/_scale_by_grad_norm_test.py
@@ -0,0 +1,45 @@
+# Copyright 2023 DeepMind Technologies Limited. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ==============================================================================
+"""Tests for `_scale_by_grad_norm.py`."""
+
+from absl.testing import absltest
+import chex
+import jax
+import jax.numpy as jnp
+from optax.contrib._scale_by_grad_norm import scale_by_gradient_norm
+
+
+class ScaleByGradientNormTest(chex.TestCase):
+  @chex.all_variants
+  def test_scale_by_gradient_norm(self):
+    params = jnp.array([300.0, -400.0])
+    updates = jnp.array([300.0, -400.0])
+
+    optim = scale_by_gradient_norm(scale=1.0)
+    init_fn = self.variant(optim.init)
+    transform_fn = self.variant(optim.update)
+
+    state = init_fn(params)
+    chex.assert_tree_all_finite(state)
+
+    updates, state = transform_fn(updates, state, params)
+    chex.assert_tree_all_finite((params, updates, state))
+    jax.tree_util.tree_map(
+	lambda *args: chex.assert_equal_shape(args), params, updates
+    )
+
+
+if __name__ == "__main__":
+  absltest.main()