The Michel parameter xi" has been determined from a measurement of the
longitudinal polarization of positrons emitted in the decay of polarized and
depolarized muons. The result, xi" = 0.981 +- 0.045stat +- 0.003syst, is
consistent with the Standard Model prediction of unity, and provides an order
of magnitude improvement in the relative precision of this parameter. This
value sets new constraints on exotic couplings beyond the dominant V-A
description of the leptonic weak interaction.Comment: 15 pages, 16 figures, 3 tables; submitted to Phys. Rev.