  In this note, we evaluate the Weyl-invariant quadratic curvature tensors for
the particular Weyl's gauge field constructed in the $3+1$-dimensional
noncompact Weyl-Einstein-Yang-Mills model. We subsequently extend the model to
its higher curvature version. Here, we also compute Weyl-invariant extension of
topological Gauss-Bonnet term for this specific choice of vector field.
