  We provide a new closed form expression for the Geronimus polynomials on the
unit circle and use it to obtain new results and formulas. Among our results is
a universality result at an endpoint of an arc for polynomials orthogonal with
respect to a Geronimus type weight on an arc of the unit circle. The key tool
is a formula of McLaughlin for powers of a two-by-two matrix, which we use to
derive convenient formulas for Geronimus polynomials.
