We present a new approach to the blind detection of full rate space-time block coded transmissions. Our method is based on linear programming and is globally convergent. We exploit the implicit structure of space-time block codes to cast the problem as linear programming to be solved efficiently. Unlike several known methods, the proposed technique is applicable to full-rate space-time block codes such as the popular Alamouti orthogonal code and the quasi-orthogonal space time code. Moreover, we utilize the code structure of these full rate codes to achieve simultaneous detection of all coded data streams without relying on successive schemes that are prone to error propagation. For orthogonal space-time codes, our algorithm allows near maximum likelihood detection of orthogonal codes without channel knowledge. We also can generalize the application of the proposed receiver to be used with nonorthogonal codes. Our proposed algorithm can provide performance competitive with existing techniques without imposing any conditions on the number of receive antennas.