Massive MIMO antennas in cellular systems help support a large number of users in the same time-frequency resource and also provide significant array gain for uplink reception. However, channel estimation in such large antenna systems can be tricky, not only since pilot assignment for multiple users is challenging, but also because the pilot overhead especially for rapidly changing channels can diminish the system throughput quite significantly. A pilotless transceiver where the receiver can perform blind demodulation can solve these issues and boost system throughput by eliminating the need for pilots in channel estimation. In this paper, we propose an iterative matrix decomposition algorithm for the blind demodulation of massive MIMO OFDM signals. This new decomposition technique provides estimates of both the user symbols and the user channel in the frequency domain simultaneously (to a scaling factor) without any pilots. Simulation results demonstrate that the lack of pilots does not affect the error performance of the proposed algorithm when compared to maximal-ratio-combining (MRC) with pilot-based channel estimation across a wide range of signal strengths.