Towards Higher Precision Measurements of the Muon Decay Parameters by TWIST

The TWIST experiment has just published its first results for the Muon Decay Parameters $\rho = 0.75080 \pm 0.00032(stat.) \pm 0.00097(syst.) \pm 0.00023(\eta)$ and $\delta = 0.74964 \pm 0.00066(stat.) \pm 0.00112(syst.)$. These results limit any possible deviations from the Standard Model predictions for these parameters by a precision 2 to 3 times better than the previous results. This talk will discuss the next phase of the experiment, which will include higher statistical precision and reduced systematic uncertainties.