In this paper, the authors consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meets pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using memorization theory, they simplify the matrix-valued optimization problem into a scalar-valued one. They then propose a lower bound and an upper bound of the original problem, both in convex forms. Specifically, the latter is solved by a multi-level water-filling algorithm that is much efficient than directly applying the interior point method.