  The discussion of renormalization group flows in four-dimensional conformal
field theories has recently focused on the a-anomaly. It has recently been
shown that there is a monotonic decreasing function which interpolates between
the ultraviolet and infrared fixed points such that \Delta a = a_UV - a_IR > 0.
The analysis has been extended to weakly relevant and marginal deformations,
though there are few explicit examples involving interacting theories. In this
paper we examine the a-theorem in the context of the gauged vector model which
couples the usual vector model to the Banks-Zaks model. We consider the model
to leading order in the 1/N expansion, all orders in the coupling constant
\lambda, and to second order in g^2. The model has both an IR and UV fixed
point, and satisfies \Delta a > 0.
