We propose a method for obtaining focal mechanisms of earthquakes recorded on a local network. It is based on the non-linear estimation of the probability function for strike, dip and slip of the focal mechanism from P polarities, S polarizations and S/P amplitude ratios. The method is shown to be effective for the analysis of small earthquakes recorded by local networks. In particular, the S/P amplitude ratios bring strong constraints on fault parameters, even if large errors are present. An application to a small earthquake recorded at the volcanic zone of Campi Flegrei (Naples, Italy) during a seismic outburst is presented. ¿ American Geophysical Union 1991