In this work we propose a sparse approximation for the full covariance matrix involved in the multiple output convolution process. We exploit the fact that each of the outputs is conditional independent of all others given the input process. This leads to an approximation for the covariance matrix which keeps intact the covariances of each output and approximates the cross-covariances terms with a low rank matrix. It has a similar form to the Partially Independent Training Conditional (PITC) approximation for a single output GP.