Using multiple-input multiple-output (MIMO) relays in cooperative communication improves the data rate and reliability of the communication. The MIMO transmission, however, requires considerable resources for the detection in the relay. In particular, if a full detect-and-forward (FDF) strategy is employed, the relay needs to spend considerable resources to perform the full MIMO detection. We propose a novel cooperative partial detection (CPD) strategy to partition the detection task between the relay and the destination. CPD modifies the tree traversal of the tree-based sphere detectors in a way where there is no need to visit all the levels of the tree and only a subset of the levels; thus, a subset of the transmitted streams are visited. The destination, then, combines the source signal and the partial relay signal to perform the final detection step and recover the transmitted vector. We study and compare the performance and complexity of FDF and CPD and show that by using the CPD approach, the relay can avoid the considerable overhead of MIMO detection while helping the source-destination link to improve its performance. More specifically, in the case of a 4X4 system, the relay complexity can be reduced by up to 80% of the conventional relaying scheme.