We propose a linear precoding technique, called multiuser generalized eigenmode transmission (MGET), based on the leakage-based precoding technique. A signal-to-leakage-plus-noise (SLNR) precoding scheme is one approach for linear precoding in the multiple-input multiple-output broadcast channel that sends multiple data streams to different users in the same cell. Unfortunately, SLNR-based scheme neglects other-cell interference, which limits the performance of users at the edge of the cell. MGET addresses the shortcomings of previous SLNR-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm as well as presenting an interference-aware enhancement to SLNR precoding scheme that uses a whitening filter for interference suppression at the receiver and a novel precoder using the interference-plus-noise covariance matrix for each user at the transmitter. We consider the typical sum-power constraint (SPC). Numerical results show that the proposed MGET technique outperforms previous linear techniques.