A manually operated motor-vehicle gearbox, the gearbox including: - a primary shaft having a longitudinal axis; - a secondary shaft having a longitudinal axis; - a first reverse gear wheel on said primary shaft and a second reverse gear wheel on said secondary shaft; and - a device for synchronization of the reverse gear (RG1, RG2) comprising: - a support shaft, fixed in rotation; - an idle gear wheel configured for engagement with the first reverse gear wheel on the primary shaft and with the second reverse gear wheel on the secondary shaft, said idle gear wheel being mounted freely rotatable and axially slidable on said support shaft and having a hub that includes a first friction surface; - a synchronizer ring, which is mounted movable on said support shaft along an axial travel and is axially countered by an elastic element along said axial travel, said synchronizer ring having a second friction surface configured for engagement with said first friction surface, said synchronizer ring being moreover constrained angularly with respect to the support shaft in a way that varies according to the position thereof along the axial travel; wherein the idle gear wheel includes a first operating position along said support shaft associated to a condition of disengagement of the reverse gear (RG1, RG2), and a second operating position along said support shaft associated to a condition of engagement of the reverse gear (RG1, RG2) wherein moreover: - during operation, when a reverse gear engagement manoeuvre (RG1, RG2) is carried out, said idle gear wheel can be moved axially along said support shaft from the first operating position to the second operating position with axial drawing of said synchronizer ring along said axial travel, said drawing including an engagement of said first friction surface and said second friction surface; and - during drawing, and before the second operating position of said idle gear wheel is reached, said synchronizer ring is configured for braking a rotary movement of said idle gear wheel by engagement of said first friction surface and said second friction surface, wherein said support shaft has a longitudinal axis parallel to the longitudinal axes (XPS, XSS) of said primary shaft and secondary shaft, and the idle gear wheel is mounted so that it constantly engages with said first reverse gear wheel and can be moved axially along the support shaft for meshing with said second reverse gear wheel in the second operating position, thus defining the reverse gear (RG1, RG2). - a primary shaft having a longitudinal axis; - a secondary shaft having a longitudinal axis; - a first reverse gear wheel on said primary shaft and a second reverse gear wheel on said secondary shaft; and - a device for synchronization of the reverse gear (RG1, RG2) comprising: - a support shaft, fixed in rotation; - an idle gear wheel configured for engagement with the first reverse gear wheel on the primary shaft and with the second reverse gear wheel on the secondary shaft, said idle gear wheel being mounted freely rotatable and axially slidable on said support shaft and having a hub that includes a first friction surface; - a synchronizer ring, which is mounted movable on said support shaft along an axial travel and is axially countered by an elastic element along said axial travel, said synchronizer ring having a second friction surface configured for engagement with said first friction surface, said synchronizer ring being moreover constrained angularly with respect to the support shaft in a way that varies according to the position thereof along the axial travel; - a support shaft, fixed in rotation; - an idle gear wheel configured for engagement with the first reverse gear wheel on the primary shaft and with the second reverse gear wheel on the secondary shaft, said idle gear wheel being mounted freely rotatable and axially slidable on said support shaft and having a hub that includes a first friction surface; - a synchronizer ring, which is mounted movable on said support shaft along an axial travel and is axially countered by an elastic element along said axial travel, said synchronizer ring having a second friction surface configured for engagement with said first friction surface, said synchronizer ring being moreover constrained angularly with respect to the support shaft in a way that varies according to the position thereof along the axial travel; - during operation, when a reverse gear engagement manoeuvre (RG1, RG2) is carried out, said idle gear wheel can be moved axially along said support shaft from the first operating position to the second operating position with axial drawing of said synchronizer ring along said axial travel, said drawing including an engagement of said first friction surface and said second friction surface; and - during drawing, and before the second operating position of said idle gear wheel is reached, said synchronizer ring is configured for braking a rotary movement of said idle gear wheel by engagement of said first friction surface and said second friction surface,