We propose a new method for the determination of planetocentric coordinates of albedo details on visible disc of a spherical planet under various conditions of its illumination. The method is intended for the processing of planet images derived from ground telescopic observations. The position of a detail on a planet image is determined not relative to the centre of the planet geometric disc, but relative to the centre of an illuminated part of planet visible disc, which permits the planetary phase influence to be excluded. To determine point positions on the illuminated part of the visible disc of a planet, we applied an auxiliary coordinate system connected with equator of intensity. The formulae for transition from the auxiliary coordinate system to the planetocentric one are derived. The boundaries of the region of the possible determinations of detail coordinates on the surface of a planet are improved. The method is tested with the use of Mars' images.