Submitted to Annals of Geophysics

We investigate conceptually, analytically, and numerically the bi-ases in the estimation of the b-value of the Gutenberg-Richter law and of its uncertainty made through the least squares technique. The biases are introduced by the cumulation operation for the cumu-lative form of the Gutenberg-Richter law, by the logarithmic trans-formation, and by the measurement errors on the magnitude. We find that the least squares technique, applied to the cumulative and binned form of the Gutenberg-Richter law, produces strong bias in the b-value and its uncertainty, whose amplitudes depend on the size of the sample. Furthermore, the logarithmic transformation pro-duces two different endemic bends in the Log(N) versus M curve. This means that this plot might produce fake significant departures from the Gutenberg-Richter law. The effect of the measurement er-rors is negligible compared to those of cumulation operation and log-arithmic transformation. The results obtained show that the least squares technique should never be used to determine the slope of the Gutenberg-Richter law and its uncertainty