A grinding machine (10) for making a hole, groove and / or recess (34) in a conduit of a needle (20) near its end (32), wherein said grinding machine (10) comprises: a strip (22) that fixes in parallel alignment a plurality of needle ducts (20) and thus exposes the ends (32) of the needle ducts (20); an assembly of needle clamping means (12) for said strip (22), comprising at least two needle clamping plates (16, 18) for fixing between said strip (22); wherein the parts of said assembly of fastening means (12) that are in contact with said strip (22) are provided with covering elements of the rubber surfaces resistant to sliding, and where said assembly of fastening means (12) comprises block means of the angled support (36) for changing the position and thus the angle at which the needle ducts (20) supported by said strip (22) extend towards an abrasive surface (30) of a wheel abrasive (40). a pair of guide blocks and side blocks for supporting said strip (22) by said mounting of fastening means (12); an assembly of the abrasive wheel (28), having said abrasive wheel (40) with said abrasive surface (30) located adjacent to said assembly of fastening means (12); a mobile table (14) operatively mounted on the grinder (10), which is configured to move said mounting of fastening means (12) along it to change the position of the needle ducts (20 ) supported on said strip (22) by said mounting of fastening means (12).Una rectificadora (10) para realizar un agujero, ranura y/o rebaje (34) en un conducto de una aguja (20) próximos a su extremo (32), donde dicha rectificadora (10) comprende: una tira (22) que fija en alineación paralela una pluralidad de conductos de las agujas (20) y de esta forma expone los extremos (32) de los conductos de las agujas (20); un montaje de medios de sujeción de las agujas (12) para dicha tira (22), que comprende al menos dos placas de sujeción de las agujas (16, 18) para fijar entre estas dicha tira (22); donde las partes de dicho montaje d