The Michel parameters of the leptonic τ decays are measured using the OPAL detector at LEP. The parameters ρ ℓ , ξ ℓ , (ξδ) ℓ (with ℓ = e, µ) and η µ are extracted from the energy spectra of the charged decay leptons and from their energy-energy correlations. A new method involving a global likelihood fit of Monte Carlo generated events with complete detector simulation and background treatment has been applied to the data recorded at center-of-mass energies close to √ s = m Z 0 corresponding to an integrated luminosity of 155 pb −1 . If e-µ universality is assumed and inferring the τ polarization from neutral current data, the measured Michel parameters are: ρ = 0.781 ± 0.028 ± 0.018, ξ = 0.98 ± 0.22 ± 0.10, η = 0.027 ± 0.055 ± 0.005, ξδ = 0.65 ± 0.14 ± 0.07, where the value of η has been constrained using the published OPAL measurements of the leptonic branching ratios and the τ lifetime. Limits on non-standard coupling constants and on the masses of new gauge bosons are obtained. The results are in agreement with the V−A prediction of the Standard Model.