We propose a novel scheme for downlink beamforming design in an underlay cognitive cellular system. The beamforming design is formulated as an optimization problem with the objective of keeping the cognitive base station transmit power as well as the induced interference on the primary users, below predefined system thresholds. This is subject to providing a certain level of signal-to-interference-plus-noise ratio (SINR) to the secondary users. We then derive the corresponding semidefinite programming form for the formulated optimization problem and propose an iterative algorithm to obtain the beamforming vectors as the optimal solutions. We further analytically show the convergence of the proposed iterative algorithm. Extensive simulations verify that the proposed algorithm quickly converges to the optimal solution. We then compare the proposed scheme with a benchmarking system defined based on the previous methods proposed in the related literature. Comparisons show that the proposed algorithm outperforms the benchmarking system and induces lower interference at the primary service receivers. It is also observed that the proposed algorithm offers a higher sum rate in comparison to the benchmarking system. Simulation results further reveal that the proposed approach effectively works at a relatively high SINR level required by secondary users and strict interference threshold set by the primary system while the benchmarking system fails to do so.