In this paper, a new beam design paradigm for coordinated beamforming (CB) for current and future cellular networks is proposed based on a relaxed zero-forcing (RZF) constraint. In the conventional zero-forcing (ZF) CB, each cooperating transmitter designs its transmit beamforming matrix to null out interference to undesired receivers completely. In the proposed RZF paradigm, however, the ZF constraint is relaxed so that a tolerable amount of interference leakage to undesired receivers is allowed for the beam design at each transmitter. By relaxing the ZF constraint in such a way, transmitters have more degrees of freedom for their beam design to increase the overall data rate of the network. An efficient algorithm for the RZFCB is proposed based on a projected subgradient method. Numerical results show that the proposed RZFCB shows a noticeable gain over the conventional ZFCB.