The main objective of this work is to present (and test with real data) a Faraday Rotation image reconstruction method for the active nucleus of M87, which could be useful in the case of weak sources and/or with small rotation measure. To achieve this, from a subset of the data generated by ALMA during the observations made by the EHT in the VLBI campaign of April 2017 (in which the first image of the vicinity of the central black hole of the galaxy M87 was obtained), ALMA images will be extracted from Stokes parameters, and we will estimate the polarization angle of M87, as well as its frequency dependency. To obtain these results, two different methods for the polarimetric analysis of radio astronomical images will be used; in addition to the standard method of Faraday synthesis, this project will develop a new algorithm, based on the Taylor series development of Stokes parameters in frequency space. Thus, from observations of a high scientific value, the first Faraday Rotation image of M87 at millimeter wavelengths will be obtained, and by comparing the results of the Faraday synthesis method, we will study the usefulness of the new algorithm developed.