We propose a multiscale method to map the spatial variations of the com- pleteness magnitude Mc of earthquake catalogs. The Gutenberg-Richter law describ- ing the earthquake frequency-magnitude distribution (FMD) might not hold over the entire magnitude range, and small areas may exhibit a specific type of seismicity, especially in volcanotectonic contexts. For these reasons, any scaling relation should be obtained by adapting the dimension of the studied zone to the range of the event magnitude. Here, we associate ranges of larger magnitudes with increasing areas for data selection based on empirical relations in seismotectonics. Then, for each point in space, we document the earthquake FMD at all length scales within the corresponding earthquake magnitude ranges. High resolution of the Mc-value is achieved through the determination of the smallest space-magnitude scale in which the Gutenberg-Richter law is verified. The multiscale procedure isolates the magnitude range that meets the best local seismicity and local record capacity. Using artificial catalogs and earthquake catalogs of the Lesser Antilles arc, this Mc-mapping method is shown to be efficient in regions with mixed types of seismicity, a variable density of epicenters, and various levels of registration.