A multiple-beam cyclic interferometer with unidirectional trajectories is presented and discussed conceptually. The main feature of the device is the utilization of controllable losses in the setup to modify conveniently the form of the fringes. Sufficient reduction of the losses results in finer and more contrasting fringes than those of a Fabry-Perot with comparable surface reflectance. The design is derived from a two-beam interferometer, and the procedure can be extended and used with other two-beam devices with division of amplitude.