We consider the two-species Lotka-Volterra competition system with a temporally periodic interruption of competition coefficient. We assume that the competition coefficient is constant in a time interval of fixed length τ+, while it is zero in the other time interval of length τ-. The temporal variation of the competition coefficient is rigorously periodic with period τ+ + τ-, in which the competition coefficient becomes a given positive constant and zero by turns, the other parameters being constant in time. We analyze the system analytically and numerically, and derive the condition for the permanence of the whole system, the coexistence of two competing species, and the change of the species-dominance in terms of the competition. We discuss some interesting natures of our system, distinguished from the original two-species Lotka-Volterra competition system with constant competition coefficients. The temporal interruption of competition could cause the change of the destiny of competing species.