Neuronal firing rate has been the signal of choice for invasive motor brain machine interfaces (BMI). The use of local field potentials (LFP) in BMI experiments may provide additional dendritic information about movement intent and may improve performance. Here we study the time-varying amplitude modulated relationship between local field potentials (LFP) and single unit activity (SUA) in the motor cortex. We record LFP and SUA in the primary motor cortex of rats trained to perform a lever pressing task, and evaluate the correlation between pairs of peri-event time histograms (PETH) and movement evoked local field potentials (mEP) at the same electrode. Three different correlation coefficients were calculated and compared between the neuronal PETH and the magnitude and power of the mEP. Correlation as high as 0.7 for some neurons occurred between the PETH and the mEP magnitude. As expected, the correlations between the single trial LFP and SUV are much lower due to the inherent variability of both signals.