This article addresses the correction for aerosol effects in near-simultaneous multi-angle observations acquired by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) aboard the Mars Reconnaissance Orbiter. In the targeted mode, CRISM senses the surface of Mars using 11 viewing angles, which allow it to provide unique information on the scattering properties of surface materials. In order to retrieve these data, however, appropriate strategies must be used to compensate the signal sensed by CRISM for aerosol contribution. This correction is particularly challenging as the photometric curve of these suspended particles is often correlated with the also anisotropic photometric curve of materials at the surface. This article puts forward an innovative radiative transfer-based method named Multi-angle Approach for Retrieval of Surface Reflectance from CRISM Observations (MARS-ReCO). The proposed method retrieves photometric curves of surface materials in reflectance units after removing aerosol contribution. MARS-ReCO represents a substantial improvement regarding previous techniques as it takes into consideration the anisotropy of the surface, thus providing more realistic surface products. Furthermore, MARS-ReCO is fast and provides error bars on the retrieved surface reflectance. The validity and accuracy of MARS-ReCO is explored in a sensitivity analysis based on realistic synthetic data. According to experiments, MARS-ReCO provides accurate results (up to 10% reflectance error) under favorable acquisition conditions. In the companion article, photometric properties of Martian materials are retrieved using MARS-ReCO and validated using in situ measurements acquired during the Mars Exploration Rovers mission.