We address the problem of designing a waveform for Multiple-Input Multiple-Output (MIMO) radar under important practical constraints, namely the constant modulus and the waveform similarity constraints. Incorporating these constraints in an analytically tractable manner continues to be longstanding open challenge. This is because the optimization problem that results from Signal to Interference plus Noise Ratio (SINR) maximization subject to these constraints is a hard non-convex problem. We develop a new analytical approach that involves solving a sequence of convex Quadratic Constrained Quadratic Programing (QCQP) problems, which we prove converges to a sub-optimal solution. We call the method Successive QCQP Refinement (SQR). We evaluate SQR against state of the art in its SINR performance for a practical scenario and show that it outperforms existing methods without incurring a significant computational burden.