A hydrostatic axial piston machine is disclosed, in the housing of which a drive shaft is rotatably mounted about an axis of rotation. The housing comprises a pot-like housing part having a first abutment and a cover-like housing part having a second abutment. The two abutments are clamped against one another in a sealing manner. A first fitting pin is inserted precisely into a first fitting recess of the first abutment on the one hand and into a second fitting recess of the second abutment on the other hand. A second fitting pin is provided on a side opposite the axis of rotation, which is inserted precisely into a third fitting recess of the first abutment on the one hand and into a fourth fitting recess of the second abutment on the other hand. The second fitting recess has a radial widening relative to the axis of rotation, whereby the second fitting recess is a slotted hole and/or a fitting groove.