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A status report is given on an experiment started in 1987 at PSI to search for the lepton flavour violating muon to electron conversion process. The motivation for this experiment, the design and performance of the detector (SINDRUM II), and results of a first run are presented. No candidate of the process mu -Ti to e-Ti was found, and, using two independent determinations of the muon stop rate, an upper limit for the branching ratio relative to muon capture Bmu e<4.4.10-12 (90% C.L.) was obtained. This result confirms the current best value for the upper limit found at TRIUMF (4.6.10-12).