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 said mounting 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) are extend towards an abrasive surface (30) of an abrasive wheel (40). 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 dicho montaje de medios de sujeción (12) comprende unos medios de bloque del soporte en ángulo (36) para cambiar la posición y de este modo el ángulo al cual los conductos de las agujas (20) apoyados mediante dicha tira (22) se extienden hacia una superficie abrasiva (30) de una muela abrasiva (40). un montaje de la r