Massive MIMO systems have made significant progress in increasing spectral and energy efficiency over traditional MIMO systems by exploiting large antenna arrays. In this paper we consider the joint maximum likelihood (ML) channel estimation and data detection problem for massive SIMO (single input multiple output) wireless systems. Despite the large number of unknown channel coefficients for massive SIMO systems, we improve an algorithm to achieve the exact ML non-coherent data detection with a low expected complexity. We show that the expected computational complexity of this algorithm is linear in the number of receive antennas and polynomial in channel coherence time. Simulation results show the performance gain of the optimal non-coherent data detection with a low computational complexity.