A novel Coordinated Interference-aware Beamforming (CIB) technique for Multiple-Input-Multiple-Output (MIMO) Broadcast Channels (BC) is introduced. The CIB technique uses a method based on maximization of the Signal to Interference and Noise Ratio (SINR) at the front end of each receiver to balance the signal strength and the multi-user interference plus noise. This results in a closed form solution that can be used with any number of transmit and receive antennas. The resulting computational complexity is not more than well known non-iterative linear beamforming techniques. The new technique, even when equal power is assigned to each data stream, outperforms the sum rate achieved by the non-iterative linear beamforming techniques when employing waterfilling power allocation. Optimality of CIB is analyzed in some extreme cases of Signal to Noise Ratio (SNR) and the number of users. In contract to the intuition that Block Diagonalization Zero Forcing (BDZF) and other ZF techniques perform very well in large number of users since they are designed for canceling interuser interference, the sum rate of the proposed CIB grows faster than ZF. Additionally, the CIB provides more flexibility when employing further upper layer scheduling algorithms by supporting both diversity and spatial multiplexing for each user.