In this paper, polynomials orthogonal on the unit circle with respect to the complex valued measure \(d(\lambda ,\eta ,\theta )= e^{(\eta +i\lambda )\theta }d\theta \) are investigated. In particular, their Christoffel transform and the associated kernel polynomials are constructed. In addition to various structural properties, the orthogonality relations are studied. Further, these polynomials are related to well-known families of orthogonal polynomials for specific values of the parameter \(\lambda \) .
