diff --git a/optax/contrib/_muon.py b/optax/contrib/_muon.py
index 5b4de8ac..d5c6a05d 100644
--- a/optax/contrib/_muon.py
+++ b/optax/contrib/_muon.py
@@ -97,6 +97,7 @@ class MuonState(NamedTuple):
   """State for the Adam algorithm."""
   count: chex.Array  # shape=(), dtype=jnp.int32.
   mu: base.Updates
+  ns_coeffs: chex.Array  # shape=(), dtype=jnp.int32.
 
 
 def scale_by_muon(
@@ -142,15 +143,19 @@ def scale_by_muon(
     <https://arxiv.org/abs/2409.20325>`_, 2024
   """
   mu_dtype = utils.canonicalize_dtype(mu_dtype)
-  ns_coeffs_ = jnp.asarray(ns_coeffs)
-  if ns_coeffs_.ndim > 2 or ns_coeffs_.shape[-1] != 3:
-    raise ValueError(
-        f'ns_coeffs must have shape (3,) or (n, 3), got {ns_coeffs_.shape}'
-    )
 
   def init_fn(params):
     mu = otu.tree_zeros_like(params, dtype=mu_dtype)  # First moment
-    return MuonState(count=jnp.zeros([], jnp.int32), mu=mu)
+    ns_coeffs_ = jnp.asarray(ns_coeffs)
+    if ns_coeffs_.ndim > 2 or ns_coeffs_.shape[-1] != 3:
+      raise ValueError(
+          f'ns_coeffs must have shape (3,) or (n, 3), got {ns_coeffs_.shape}'
+      )
+    return MuonState(
+        count=jnp.zeros([], jnp.int32),
+        mu=mu,
+        ns_coeffs=ns_coeffs_,
+    )
 
   def update_fn(updates, state, params=None):
     del params
@@ -168,7 +173,9 @@ def update_fn(updates, state, params=None):
       mu_hat = otu.tree_bias_correction(mu, beta, count_inc)
     # Apply Newton-schulz orthogonalization.
     updates = jax.tree.map(
-        lambda x: orthogonalize_via_newton_schulz(x, ns_coeffs_, ns_steps, eps),
+        lambda x: orthogonalize_via_newton_schulz(
+            x, state.ns_coeffs, ns_steps, eps
+        ),
         mu_hat,
     )
     if adaptive:
@@ -178,7 +185,11 @@ def update_fn(updates, state, params=None):
           lambda x, y: jnp.einsum('ij,ij,ab->ab', x, y, y), mu_hat, updates
       )
     mu = otu.tree_cast(mu, mu_dtype)
-    return updates, MuonState(count=count_inc, mu=mu)
+    return updates, MuonState(
+        count=count_inc,
+        mu=mu,
+        ns_coeffs=state.ns_coeffs,
+    )
   return base.GradientTransformation(init_fn, update_fn)