Motor vehicle disc brake including: - a cover including two tiered bores of parallel axes, each whereof includes at least one first section (28, 30); - a caliper slidably mounted axially with respect to the cover; - two pins (16, 18) of parallel axes (A, B), each whereof includes: -- an axial attachment end (20, 22) attached to the caliper; and -- at least one guiding section (24, 26) for axial sliding of the caliper with respect to the cover which extends from a free end (25, 27) of the associated pin (16, 18) which is facing a base (33, 35) of said first section (28, 30), said guiding section being slidably mounted in the first section (28, 30) of the associated tiered bore (29, 31) of the cover, characterised in that: - each pin (16, 18) includes at least one flat section extending from the free end (25, 27) of the pin along a length greater than that of said guiding section (24, 26) and which, engaging with the wall of the bore (29, 31), defines at least one axial channel extending from said free end (25, 27) of the pin, in which said channel communicates with the space defined by said base (33, 35), by the lateral wall of the bore and by a transverse face of the free end (25, 27) of the pin (16, 18), - the associated tiered bore (29, 31) of the cover includes, on the side of the end (20, 22) for attaching the pin (16, 18) to the caliper, a second section (46, 48), - each pin (16, 18) receives a tubular sealing cap (32, 34) wherein one section (42, 44) is inserted radially between the associated pin (16, 18), and said second section (46, 48) and - an inner wall of each tubular cap (32, 34) includes at least one radial groove or a radial channel communicating with said at least one axial channel defined by the associated pin. - a cover including two tiered bores of parallel axes, each whereof includes at least one first section (28, 30); - a caliper slidably mounted axially with respect to the cover; - two pins (16, 18) of parallel axes (A, B), each whereof includes: -- an axial attachment end (20, 22) attached to the caliper; and -- at least one guiding section (24, 26) for axial sliding of the caliper with respect to the cover which extends from a free end (25, 27) of the associated pin (16, 18) which is facing a base (33, 35) of said first section (28, 30), said guiding section being slidably mounted in the first section (28, 30) of the associated tiered bore (29, 31) of the cover, characterised in that: - each pin (16, 18) includes at least one flat section extending from the free end (25, 27) of the pin along a length greater than that of said guiding section (24, 26) and which, engaging with the wall of the bore (29, 31), defines at least one axial channel extending from said free end (25, 27) of the pin, in which said channel communicates with the space defined by said base (33, 35), by the lateral wall of the bore and by a transverse face of the free end (25, 27) of the pin (16, 18), - the associated tiered bore (29, 31) of the cover includes, on the side of the end (20, 22) for attaching the pin (16, 18) to the caliper, a second section (46, 48), - each pin (16, 18) receives a tubular sealing cap (32, 34) wherein one section (42, 44) is inserted radially between the associated pin (16, 18), and said second section (46, 48) and - an inner wall of each tubular cap (32, 34) includes at least one radial groove or a radial channel communicating with said at least one axial channel defined by the associated pin. -- an axial attachment end (20, 22) attached to the caliper; and -- at least one guiding section (24, 26) for axial sliding of the caliper with respect to the cover which extends from a free end (25, 27) of the associated pin (16, 18) which is facing a base (33, 35) of said first section (28, 30), said guiding section being slidably mounted in the first section (28, 30) of the associated tiered bore (29, 31) of the cover, - each pin (16, 18) includes at least one flat section extending from the free end (25, 27) of the pin along a length greater than that of said guiding section (24, 26) and which, engaging with the wall of the bore (29, 31), defines at least one axial channel extending from said free end (25, 27) of the pin, in which said channel communicates with the space defined by said base (33, 35), by the lateral wall of the bore and by a transverse face of the free end (25, 27) of the pin (16, 18), - the associated tiered bore (29, 31) of the cover includes, on the side of the end (20, 22) for attaching the pin (16, 18) to the caliper, a second section (46, 48), - each pin (16, 18) receives a tubular sealing cap (32, 34) wherein one section (42, 44) is inserted radially between the associated pin (16, 18), and said second section (46, 48) and - an inner wall of each tubular cap (32, 34) includes at least one radial groove or a radial channel communicating with said at least one axial channel defined by the associated pin.