We propose a novel scheme to design downlink beamforming vectors in a cognitive cellular network which shares radio spectrum with a primary communication system. We formulate an optimization problem which minimizes the cognitive base station transmit power and the induced interference on the primary users and keeps them below predefined system thresholds. This is subject to providing a certain level of signal-to-interference-plus-noise ratio to the secondary users. We propose an iterative algorithm to solve the optimization problem. The convergence of the proposed iterative algorithm is analytically proved. Simulation results verify that the proposed algorithm quickly converges to the optimal solution. Results also indicate that the proposed algorithm guarantees the transmit power and interference constraints. We then compare the proposed scheme with a benchmark system based on the previous methods. Comparisons show significant reduction in the total interference at reasonable cost of the cognitive base station transmit power.