Previous measurements of the branching fractions of the tau lepton result in a discrepancy between the inclusive branching fraction and the sum of the exclusive branching fractions to final states containing one charged particle. The sum of the exclusive branching fractions is significantly smaller than the inclusive branching fraction. In this analysis, the branching fractions for all the major decay modes are measured simultaneously with the sum of the branching fractions constrained to be one. The branching fractions are measured using an unbiased sample of tau decays, with little background, selected from 207 pb−1 of data accumulated with the Mark II detector at the PEP ee− storage ring. The sample is selected using the decay products of one member of the .gamma.gamma.− pair produced in e+e− annihilation to identify the event and then including the opposite member of the pair in the sample. The sample is divided into subgroups according to charged and neutral particle multiplicity, and charged particle identification. The branching fractions are simultaneously measured using an unfold technique and a maximum likelihood fit. The results of this analysis indicate that the discrepancy found in previous experiments is possibly due to two sources. First, the leptonic branching fractions measured in this analysis are about one standard deviation higher than the world average. The measured leptonic branching fractions correspond to a tau lifetime of (3.0 +- 0.2) x 10−13 s. Secondly, the total branching fraction to one charged hadron plus at least one neutral particle is measured to be (7 +- 3)% higher than the branching fraction expected from a combination of previous measurements and theoretical predictions. It is shown that decay modes involving the eta are not expected to contribute more than 3% to this excess.