We study the decay of the metastable symmetric phase in the standard model at finite temperature. For the SU(2)-Higgs model the two wave function correction terms Z_#phi#(#phi#"2,T) and Z_#chi#(#phi#"2,T) of Higgs and Goldstone boson fields are calculated to one-loop order. We find that the derivative expansion of the effective action is reliable for Higgs masses smaller than the W-boson mass. We propose a new procedure to evaluate the decay rate by first integrating out the vector field and the components of the scalar fields with non-zero Matsubara frequencies. The static part of the scalar field is treated in the saddle point approximation. As a by-product we obtain a formula for the decay rate of a homogeneous unstable state. ...