An assembly for a caliper of a disc brake, wherein, when said caliper is arranged astride a disc of a disc brake having a defined rotation axis, said assembly defines an axial direction (X-X) parallel to said rotation axis, a radial direction (R-R) orthogonal to said axial direction (X-X) and a tangential or circumferential direction (T-T) orthogonal to both the axial direction (X-X) and the radial direction (R-R), said assembly comprising: - a first pad comprising a friction material, defining a friction surface, and a support plate which supports said friction material and is adapted to release the braking action onto the caliper of the disc brake, wherein - said support plate comprises at least one lateral projection which extends in a direction substantially coplanar to the plate and is placed at an end of the support plate, and wherein - said at least one lateral projection is adapted to be accommodated in a pocket obtained in the body of the caliper; - said assembly further comprising at least one spring, wherein said spring is connected to said lateral projection of said support plate, and wherein - said spring being adapted to be accommodated in a seat formed in the body of the caliper at said pocket, said seat being delimited by at least one seat wall, - said support plate comprises at least one pair of opposite lateral projections which extend in direction substantially coplanar with the plate and are placed at opposite ends of the support plate, and said assembly comprises at least one pair of springs, wherein each spring is connected to each lateral projection of said plate, and wherein - each of said springs is adapted to be inserted in a respective seat to be fastened onto said seat wall to bias said pad in axial direction (X-X); characterized in that each spring comprises at least two mutually opposed elastic arms adapted to be abutted against the seat wall to fasten said spring to said seat by means of a force coupling, wherein each seat has a predetermined width transverse to the longitudinal extension thereof, and wherein said at least two elastic arms are mutually opposed and, in extended condition not coupled to the seat, have at least one portion thereof which is distanced from the opposed portion of the facing arm by a distance which is greater than the predetermined transverse width of the seat, so as to guarantee a force coupling between said spring and the respective seat, so that by entering in its seat the spring elastically compresses, folding the arms, forcing onto the walls of the seat to exert a friction action in axial direction (X-X) and an elastic action in radial direction (R-R). - a first pad comprising a friction material, defining a friction surface, and a support plate which supports said friction material and is adapted to release the braking action onto the caliper of the disc brake, wherein - said support plate comprises at least one lateral projection which extends in a direction substantially coplanar to the plate and is placed at an end of the support plate, and wherein - said at least one lateral projection is adapted to be accommodated in a pocket obtained in the body of the caliper; - said assembly further comprising at least one spring, wherein said spring is connected to said lateral projection of said support plate, and wherein - said spring being adapted to be accommodated in a seat formed in the body of the caliper at said pocket, said seat being delimited by at least one seat wall, - said support plate comprises at least one pair of opposite lateral projections which extend in direction substantially coplanar with the plate and are placed at opposite ends of the support plate, and said assembly comprises at least one pair of springs, wherein each spring is connected to each lateral projection of said plate, and wherein - each of said springs is adapted to be inserted in a respective seat to be fastened onto said seat wall to bias said pad in axial direction (X-X);