  A presentation of the problem of calculating the vector coupling coefficients
for $SU3 \supset SU2 \otimes U1$ is made, in the spirit of traditional
treatments of SU2 coupling. The coefficients are defined as the overlap matrix
element between product states and a coupled state with good SU3 quantum
numbers. A technique for resolution of the outer degeneracy problem, based upon
actions of the infinitesimal generators of SU3 is developed, which
automatically produces vector coupling coefficients with symmetries under
exchange of state labels which parallel the familiar symmetries of the SU2
case. An algorithm for efficient computation of these coefficients is outlined,
for which an ANSI C code is available.
