The invention relates to a chain cutting machine and, in particular, it relates to a lubrication method of the contacting surfaces between the chain links (31) and a guide executed in the blade body, on which said chain slides. The blade body provides at least one lubricant input duct executed in the blade body through a channel that extends parallel to the perimeter of the blade, and a plurality of holes that connect said channel with the sliding zone. According to another aspect, each link of the chain comprises a cutting tip holder (11) that holds at least one cutting tip (12), equipped with engagement means (14), so called brackets, for connecting the cutting tips (12) to said cutting tip holders (11) by friction caused by the pressure of the bracket (14). This way, for changing a worn cutting edge it is not necessary to unscrew completely the fastening screw (15) of the cutting tip, but a few unscrewing turns are enough for loosening the cutting tip and changing its position.