A theoretical and experimental analysis of a spatial instability developing in a homeotropically aligned nematic liquid crystal film is presented. The explanation for the existence of this instability is supplied through an amplitude equation. This model, which is valid in the vicinity of the Fréedericksz transition, assumes a strong difference between the nematic elastic constants. The first report of such an instability observed in the conditions accounted for by our model, was provided by Cladis and Torza [J. Appl. Phys. 6, 584 (1975)]. We repeated these experiments in order to confirm the validity of the model. Although carried out far from the Fréedericksz transition, these latter show a good qualitative agreement with the theoretical predictions. The nonlinear analysis allows to understand the dynamical behavior of an interface separating domains of stripes through the occurrence of a zigzag instability.