Multiple-input-multiple-output (MIMO) radar transmit beamforming mainly relies on designing transmitted signals with an appropriate covariance matrix. The signals can be designed using a two-step method which first optimizes the covariance matrix and then searches for the signals accordingly. A more efficient way is to synthesize transmitted signals by designing a weight matrix given a set of orthogonal waveforms, which makes use of both MIMO waveform diversity and phased-array transmit gain. In this paper, we propose a method to design the transmit beampattern by solving a semidefinite programming (SDP) problem. Then the eigen-decomposition of the optimal covariance matrix yields the weight matrix. Therefore it is called the SDP-EIG method. As a result, the overall transmitted waveforms are obtained more simply and efficiently, and the number of orthogonal signals required to form a desired beam reaches its minimum.