  The Conway potential function (CPF) for colored links is a convenient version
of the multi-variable Alexander-Conway polynomial. We give a skein
characterization of CPF, much simpler than the one by Murakami. In particular,
Conway's `smoothing of crossings' is not in the axioms. The proof uses a
reduction scheme in a twisted group-algebra $\mathbb P_nB_n$, where $B_n$ is a
braid group and $\mathbb P_n$ is a domain of multi-variable rational fractions.
The proof does not use computer algebra tools. An interesting by-product is a
characterization of the Alexander-Conway polynomial of knots.
