We consider the Multiple Input Single Output (MISO) Gaussian Broadcast channel with $N_t$ antennas at the base station (BS) and $N_u$ single-antenna users in the downlink. We propose a novel user grouping precoder which improves the sum rate performance of the Zero-Forcing (ZF) precoder specially when the channel is ill-conditioned. The proposed precoder partitions all the users into small groups of equal size. Downlink beamforming is then done in such a way that, at each user's receiver the interference from the signal intended for users not in its group is nulled out. Intra-group interference still remains, and is cancelled through successive interference pre-subtraction at the BS using Dirty Paper Coding (DPC). The proposed user grouping method is different from user selection, since it is a method for precoding of information to the selected (scheduled) users, and not for selecting which users are to be scheduled. Through analysis and simulations, the proposed user grouping based precoder is shown to achieve significant improvement in the achievable sum rate when compared to the ZF precoder. When users are paired (i.e., each group has two users), the complexity of the proposed precoder is $O(N_u^3) + O(N_u^2 N_t)$ which is the same as that of the ZF precoder.