A system of polishing a concave surface of an external piece for a timepiece, including a securing device including a support that carries the piece, and a grinding device including an abrasive mechanism rotatably mounted along a first axis and configured to polish the piece along a first curvature. The securing device further includes a moving mechanism of the support so that the support imparts a back-and-forth motion along a second axis and a contact surface of the abrasive mechanism is curved to polish the piece along a second curvature in addition to the first curvature. The system can be applied to the field of crystals for a timepiece.