  We apply a covariant and generic procedure to obtain explicit expressions of
the transverse frames that a type I spacetime admits in terms of an arbitrary
initial frame. We also present a simple and general algorithm to obtain the
Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these
transverse frames. In both cases it is only necessary to choose a particular
root of a cubic expression.
