diff --git a/cuequivariance/cuequivariance/descriptors/__init__.py b/cuequivariance/cuequivariance/descriptors/__init__.py
index c9592cb..af6e6e3 100644
--- a/cuequivariance/cuequivariance/descriptors/__init__.py
+++ b/cuequivariance/cuequivariance/descriptors/__init__.py
@@ -14,6 +14,7 @@
 # limitations under the License.
 from .transposition import transpose
 from .irreps_tp import (
+    full_tensor_product,
     fully_connected_tensor_product,
     channelwise_tensor_product,
     elementwise_tensor_product,
@@ -35,6 +36,7 @@
 
 __all__ = [
     "transpose",
+    "full_tensor_product",
     "fully_connected_tensor_product",
     "channelwise_tensor_product",
     "elementwise_tensor_product",
diff --git a/cuequivariance/cuequivariance/descriptors/irreps_tp.py b/cuequivariance/cuequivariance/descriptors/irreps_tp.py
index 1efdf2a..631e4c0 100644
--- a/cuequivariance/cuequivariance/descriptors/irreps_tp.py
+++ b/cuequivariance/cuequivariance/descriptors/irreps_tp.py
@@ -80,6 +80,62 @@ def fully_connected_tensor_product(
     )
 
 
+def full_tensor_product(
+    irreps1: cue.Irreps,
+    irreps2: cue.Irreps,
+    irreps3_filter: Optional[Sequence[cue.Irrep]] = None,
+) -> cue.EquivariantTensorProduct:
+    """
+    subscripts: ``lhs[iu],rhs[jv],output[kuv]``
+
+    Construct a weightless channelwise tensor product descriptor.
+
+    .. currentmodule:: cuequivariance
+
+    Args:
+        irreps1 (Irreps): Irreps of the first operand.
+        irreps2 (Irreps): Irreps of the second operand.
+        irreps3_filter (sequence of Irrep, optional): Irreps of the output to consider.
+
+    Returns:
+        EquivariantTensorProduct: Descriptor of the full tensor product.
+    """
+    G = irreps1.irrep_class
+
+    if irreps3_filter is not None:
+        irreps3_filter = into_list_of_irrep(G, irreps3_filter)
+
+    d = stp.SegmentedTensorProduct.from_subscripts("iu,jv,kuv+ijk")
+
+    for mul, ir in irreps1:
+        d.add_segment(0, (ir.dim, mul))
+    for mul, ir in irreps2:
+        d.add_segment(1, (ir.dim, mul))
+
+    irreps3 = []
+
+    for (i1, (mul1, ir1)), (i2, (mul2, ir2)) in itertools.product(
+        enumerate(irreps1), enumerate(irreps2)
+    ):
+        for ir3 in ir1 * ir2:
+            # for loop over the different solutions of the Clebsch-Gordan decomposition
+            for cg in cue.clebsch_gordan(ir1, ir2, ir3):
+                d.add_path(i1, i2, None, c=cg)
+
+                irreps3.append((mul1 * mul2, ir3))
+
+    irreps3 = cue.Irreps(G, irreps3)
+    irreps3, perm, inv = irreps3.sort()
+    d = d.permute_segments(2, inv)
+
+    d = d.normalize_paths_for_operand(-1)
+    return cue.EquivariantTensorProduct(
+        d,
+        [irreps1, irreps2, irreps3],
+        layout=cue.ir_mul,
+    )
+
+
 def channelwise_tensor_product(
     irreps1: cue.Irreps,
     irreps2: cue.Irreps,
diff --git a/cuequivariance/tests/equivariant_tensor_products_test.py b/cuequivariance/tests/equivariant_tensor_products_test.py
index a6f00bd..86126bb 100644
--- a/cuequivariance/tests/equivariant_tensor_products_test.py
+++ b/cuequivariance/tests/equivariant_tensor_products_test.py
@@ -31,6 +31,12 @@ def test_commutativity_squeeze_flatten():
         == d.flatten_coefficient_modes().squeeze_modes()
     )
 
+    d = descriptors.full_tensor_product(irreps1, irreps2, irreps3).d
+    assert (
+        d.squeeze_modes().flatten_coefficient_modes()
+        == d.flatten_coefficient_modes().squeeze_modes()
+    )
+
     d = descriptors.channelwise_tensor_product(irreps1, irreps2, irreps3).d
     assert (
         d.squeeze_modes().flatten_coefficient_modes()