The invention relates to a method for preparing an ophthalmic lens (20) for mounting the same into the rim of a rimmed spectacles frame that comprises the step of acquiring a first longitudinal profile (27) of a groove of said rim, the step of blocking the lens in a holding means, and the step of trimming the ophthalmic lens using trimming means, during which the holding and trimming means are driven so that the ophthalmic lens is trimmed and includes a fitting rib extending along a second longitudinal profile (25; 26) derived from the first longitudinal profile. According to the invention, the method comprises the step of determining a second longitudinal profile of a singular portion (Z1) having a reduced curvature radius. Furthermore, during the trimming step, the holding and trimming means are driven so that the section of the fitting rib is locally narrowed in terms of width and/or height in said singular portion, and/or so that the setpoint of the trimming radius is reduced in said singular portion.