Abstract: An idea that an arbitrary transmit beampattern can be equal to a sum of the most basic beams is proposed. Based on the idea and using the Chebyshev weighting technique, the most basic beams are constructed with low side-lobes for a Multiple Input Multiple Output (MIMO) radar system with colocated antennas. The ratios of these beams are fast obtained by solving an effective linear programming. Compared with the existing Semidefinite Quadratic Programming (SQP) method, the designed transmit beampattern can achieve lower spatial side-lobes and cross-correlation. Furthermore, it is faster to design the transmit beampattern.