A simple tetrahedron model is used to study the effect of non-Gaussian chains on fluctuations of junctions in bimodal networks. The four chains are assumed to meet at a junction with their other ends being fixed at the vertices of the tetrahedron. It is assumed that the angles between mean end-to-end vectors of all four chains connected at the junction are tetrahedral, but the lengths of edges of the tetrahedron may differ due to the difference in the lengths of the chains. The central junction is free to fluctuate, subject to the constraints imposed by the pendant chains. The long chains are chosen to be Gaussian. The short chains are assumed to be non-Gaussian. Calculations show that the non-Gaussian nature of the short chains imposes severe restrictions on the fluctuations of the central junction. The strength of these restrictions directs attention to the importance of anharmonic modes in networks.