Summary: Spatial Multiplexing (SM) is an effective means for enhancing the transmission data rate in Multiple-Input Multiple-Output (MIMO) systems, particularly when used in combination with precoding techniques. However, it is not always obvious to connect the performance of such a system to its number of data streams and antennas. In this paper, the diversity order of a SM MIMO system using a Minimum Mean Square Error (MMSE) receiver is analytically calculated when a precoder based on transmit antenna correlation is included at the transmitter. It is shown that it is given by $d = N _{r } - N _{s } + 1$ where $N _{r }$ is the number of receive antennas and $N _{s }$ is the number of data streams. This result is confirmed by simulations. Although enabling a Signal-to-Noise Ratio (SNR) gain, such a precoder is thus not able to improve the diversity order with respect to a non-precoded SM MIMO system.