The present invention belongs to the technological field of the head fastening and its components to the block of a compressor, such as those used in cooling systems of household appliances. The head fastening arrangement of cooling compressor includes a head arranged by the cylinder of the cooling compressor and having a head lid; at least one supporting device also arranged by the cylinder; at least one element of union of the head lid to the supporting device, wherein the element of union is capable of transmitting force that presses the head lid and the supporting device against the cylinder.