diff --git a/src/skillmodels/qr.py b/src/skillmodels/qr.py
index c690eac7..965b9cc3 100644
--- a/src/skillmodels/qr.py
+++ b/src/skillmodels/qr.py
@@ -19,16 +19,13 @@ def _householder(r: jax.Array, tau: jax.Array):
     """
     m = r.shape[0]
     n = tau.shape[0]
+    r = jnp.tril(jnp.fill_diagonal(r, 1, inplace=False))
     # Calculate Householder Vector which is saved in the lower triangle of R
     v1 = jnp.expand_dims(r[:, 0], 1)
-    v1 = v1.at[0:0].set(0)
-    v1 = v1.at[0].set(1)
     h = jnp.eye(m) - tau[0] * (v1 @ jnp.transpose(v1))
     # Multiply all Householder Vectors Q = H(1)*H(2)...*H(n)
     for i in range(1, n):
         vi = jnp.expand_dims(r[:, i], 1)
-        vi = vi.at[0:i].set(0)
-        vi = vi.at[i].set(1)
         h = h - tau[i] * (h @ vi) @ jnp.transpose(vi)
     return h[:, :n]