The conventional amplify-and-forward cooperative system is capable of achieving a superior performance with the aid of Multiple-Symbol Differential Sphere Detection (MSDSD), when compared to conventional differential detection (CDD) for transmission over time-selective channels. However, the conventional broadcast/cooperative twin-phase based relaying protocol encounters a 50% throughput loss imposed by half-duplex relaying. For combating this problem, in this paper, we create a MSDSD aided successive relaying based cooperative DS-CDMA system. We demonstrate that given the target BER of 10-4, a diversity gain of up to 10 dB is achieved over the benchmark schemes employed without a throughput loss.