Designing transmit beampattern with MIMO radars generally requires the waveforms to be able to have arbitrary cross-correlation values. In contrast to the available algorithms, the proposed technique provides a closed-form solution for the synthesis of covariance matrix, R, of the waveforms to obtain desired beampattern match. To synthesis R the constraints and redundant information in R are leveraged, which convert the constrained problem into un-constrained problem. Next a novel method for generating the constant-envelope (CE) waveforms to realise the synthesised covariance matrix, R, is proposed. This method also yields a closed-form solution and choose the symbols from the binary-phase shift-keying (BPSK). Here, Gaussian random-variables (RV's) are mapped onto the CE RV's by a memoryless non-linear transformation, which converts the problem of finding the non-Gaussian RV's to realise a given covariance matrix R into finding the Gaussian RV's to realise covariance matrix Rg. Simulation results are presented to demonstrate the effectiveness of both methodologies.