Designing paraunitary filter banks (PUFBs) that minimize a mean squared error (MMSE) design criterion and are globally optimal is a difficult problem in nonlinear optimization. Many techniques have been proposed to simplify this problem including the use of reduced parameter PUFB decompositions to reduce the complexity of the nonlinear program. In this paper, a simple yet effective method is presented for designing PUFBs that satisfy an approximated MMSE criterion with the caveat that the paraunitary condition is satisfied only on a discrete set of frequencies. No statement can be made about the performance or the losslessness of the designed filter bank between selected frequency points, but for a sufficiently large grid with a dense distribution of points, the proposed design method may yield adequate performance in practical situations.