Several general evolutionary approaches have proven quite successful at evolving teams (or ensembles) consisting of cooperating team members. However, in this paper we demonstrate that the existing approaches have subtle, but significant, weaknesses. We then present a novel class of evolutionary algorithms (orthogonal evolution of teams (OET)) for evolving teams that overcomes these weaknesses. Specifically it is shown that a typical algorithm from the OET class of algorithms successfully generates team members that have fitnesses comparable to those evolved independently and that have inversely correlated errors, which maximizes the teams’ overall performance. Finally it is shown that the OET approach performs significantly better than the standard evolutionary approaches.