The majority of fMRI studies obtain functional information using statistical tests based on the magnitude image reconstructions. Recently, a complex correlation (CC) test was proposed based on teh complex image data in order to take advantage of phase information in teh signal. However, the CC test ignores additional phase information in the baseline component of the data. In this paper, a new detector for fMRI based on a Generalized Likelihood Ration Test (GLRT) is proposed. The GLRT exploits the fact that the fMRI response signal as well as the baseline component of the data share a common phase. Theoretical analysis and Monte Carlo simulation are used to explore the performance of the new detector. At relatively low signal intensities, the GLRT outperforms both the standard magnitude data test and the CC test. At high signal intensities, the GLRT performs as well as teh standard magnitude data test and significantly better than the CC test.