The paper presents a new procedure to design a two-pulley synchronous belt transmission connecting, with no belt tensioner, two parallel-axis shafts with a variable velocity ratio. The procedure takes into account the limited number of choices for pitch and length of off-the-shelf synchronous belts, which translates into the need of fine-adjusting either the center distance or the law of motion. Differently from other approaches reported in the technical literature, the suggested method is based on the numerical solution of a set of functional equations. A numerical example shows application of the proposed method to a case study.