All possible one-component delocalized nonlinear vibrational modes (DNVMs) in a square lattice are analyzed. DNVMs are obtained taking into account exclusively the symmetry of a square lattice, and therefore they exist regardless of the type of interactions between particles. In this work, the interactions of the nearest and next nearest neighbors are described by the β-FPU potential. For each DNVM, frequency, kinetic and potential energies are described as functions of amplitude. The mechanical stresses caused by DNVMs and the effect of DNVMs on the stiffness constants of the lattice are presented. DNVMs with higher vibration frequencies have a stronger effect on the mechanical properties of the lattice. Examples of analytical analysis of DNVMs are given. It is found that two of the sixteen one-component DNVMs can have frequencies above the phonon band in the entire range of their amplitudes. These DNVMs can be used to construct discrete breathers by applying localizing functions.