The branching fraction of the ψ(2S) decay into τ+τ - has been measured for the first time using the BES detector at the Beijing Electron-Positron Collider. The result is Bττ=(2.710. 43±0.55)× 10-3, where the first error is statistical and the second is systematic. This value, along with those for the branching fractions into e+e- and μ+ μ- of this resonance, satisfy well the relation predicted by the sequential lepton hypothesis. Combining all these values with the leptonic width of the resonance, the total width of the ψ(25) is determined to be (252±37) keV. ©2002 The American Physical Society.