A new design of the laser resonator using dual phase conjugation mirrors is discussed. It is shown that using the modified Gerchberg-Saxton algorithm, phase conjugation criteria at the both mirrors with finite apertures can be met for the given shape of desired mode. The flexibility of the design method allows the method can be applied to any other resonator design using either transmissive or reflective element(s) inside the cavity to satisfy the given amplitude/phase requirement of desired mode at any location. Unlike previous studies on the phase conjugation resonators, the new dual phase conjugation resonator is shown to provide extremely low loss for the desired mode while providing higher discrimination against the higher order modes. This approach to designing a resonator has been applied to the design of a large Fresnel number cavity for a ideal diode pumped laser with the objective achieving a large filling factor with a single mode and a design example will be presented.