A hydraulic piston machine including a housing, a shaft that is able to rotate relative to the housing, and a cam secured to one of the housing or the shaft. A cylinder block includes pistons that are able to move in the cylinder block opposite the cam in order to generate relative rotation between the cylinder block and the cam. The cylinder block is linked in rotation to the other of the shaft or the housing. A mechanism forms rotation guide bearings for guiding the rotation of the shaft relative to the housing, which mechanism includes a tapered plain bushing interposed between a housing element and an element linked in rotation with the shaft and in which the tapered plain bushing includes a radial through-slit extending through the entire radial dimension of the bushing.