In this paper we propose an inverse QR decomposition based recursive least squares algorithm (IQRD-RLS) for the linearly constrained minimum variance (LCMV) receiver for CDMA transmission systems. The proposed algorithm is numerically stable and it is suitable for implementation in systolic arrays or DSP vector architectures. It is shown through computer simulations that the proposed algorithm outperforms, in terms of bit error rate, previously proposed IQRD-RLS based blind detection algorithms.