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We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued into a branch of travelling corners. As an example, we consider the monochromatic and bichromatic Nagumo lattice differential equation and show that both systems exhibit interior and exterior corners. Our result is valid in the setting where the group velocity is zero. In this case, the equations for the corner can bedoi:10.3934/cpaa.2020058 fatcat:2fkmlmx4yvdsphotz5b3gqcetm