This paper presents a simply change of basis technique for transforming one type of Pólya curves to another closely related Pólya curve form. Repeated use of this method yields algorithms for transforming one arbitrary Pólya form to another, as well as algorithms for evaluating, subdividing and differentiating Pólya curves. These procedures can be applied to almost all Pólya curves, including Bézier curves and Lagrange interpolating polynomials.