A new reference attenuation model for calculating local magnitude () for New Zealand earthquakes is derived. An earlier reference model, denoted NZ16, was developed in 2016 as a possible alternative to the classical reference model used by GeoNet for earthquakes located by the SeisComP processing system since January 2012. It aimed to provide a attenuation relation of the amplitude with the hypocentral distance applicable to the New Zealand region and to make more consistent with moment magnitude (). For the present update, denoted NZ20, a much larger set of regional moment tensor solutions and corresponding station amplitudes is available. Residual analysis is used to screen the individual station amplitude readings and then to exclude observations from periods of time when the station residuals were consistently anomalous. Effects of other possible sources of bias on the attenuation relation are also examined, including unreliable locations of earthquakes with large azimuthal gaps and the saturation of in large earthquakes. An extra explanatory variable is added to the attenuation relation to account for dependence on hypocentral depth, so the updated local magnitude is consistent with across the full range of depths at which earthquakes occur in New Zealand. Furthermore, to counteract possible sources of bias, the data set for analysis is restricted. Earthquakes above the approximate amplitude saturation threshold of 6.6, as well as those with azimuthal gaps greater than 270°, are excluded.