[en] The phase diagram of an Ising square lattice gas with unequal nearest- and next-nearest-neighbour repulsive interactions is investigated for a situation where the ratio R between the nearest- and the next-nearest-neighbour interaction is 0.75. Monte Carlo simulation results of the specific heat, order parameter and its susceptibility and the anisotropy of tracer diffusion coefficient are used to delineate the various phase boundaries. This system is found to exhibit degenerate (2x2)sub(+) and (2x2)sub(-) phases in a narrow range of coverages around theta=0.25 and theta=0.75 and T/phisub(nn) approx.= 0.18 and it orders in (2x1) structure in the coverage range of 0.375 to 0.625 below T/phisub(nn) approx.= 0.359. Here phisub(nn) denotes the strength of nearest-neighbour interaction. (author)