The present article describes an approach that allows a systematic analysis of nonlinear systems regarding flatness. Based on a linearization around an arbitrary trajectory, an algorithm for determining a so-called unimodular completion is proposed. In order to prove flatness and identify a flat output of the nonlinear system, this completion needs to fulfill certain integrability conditions. A freely available implementation of the algorithm is used to determine flat outputs, which is shown in the example of a gantry crane. Furthermore, in some cases, considerable simplifications may occur which is exemplified by the kinematic vehicle.