diff --git a/jax/_src/random.py b/jax/_src/random.py
index 12aa5b93efbf..f956241ce06f 100644
--- a/jax/_src/random.py
+++ b/jax/_src/random.py
@@ -2070,8 +2070,8 @@ def orthogonal(
   n = core.concrete_or_error(index, n, "The error occurred in jax.random.orthogonal()")
   z = normal(key, (*shape, n, n), dtype)
   q, r = jnp.linalg.qr(z)
-  d = jnp.diagonal(r, 0, -2, -1)
-  return lax.mul(q, lax.expand_dims(lax.div(d, abs(d).astype(d.dtype)), [-2]))
+  d = jnp.diagonal(r, axis1=-2, axis2=-1)
+  return q * jnp.expand_dims(jnp.sign(d), -2)
 
 def generalized_normal(
   key: ArrayLike,