A fixing system for fixing a connection bar for connecting layers of concrete, comprising: an upper, first housing device comprising: - a hollow body having a cylindrical extension between a first and a second end (2a, 2b) and comprising a bottom portion at said second end, said bottom portion having an opening towards the outside; - a hollow projection connected to said bottom portion so as to communicate with the opening and having an extension away from it; - a plurality of flaps arranged around the hollow body; a first plate for sharing the compressive load arranged inside the hollow body of the first housing device, one side of said first plate being in contact with the bottom portion; a second plate for sharing the tensile load at an opposite side of the first plate with respect to the bottom portion; a nut interposed between the first and the second plate (11, 12); an extension tube having an end portion inserted into the hollow projection; a further housing device, a hollow projection of which is mounted at an opposite end of the extension tube, said fixing system comprising a screwing means from above of a connection bar arranged in the further housing device, wherein said screwing means from above comprises a thick washer and a threaded portion associated therewith for the screwing from above of the connection bar, wherein said threaded portion is made in a through hole of the thick washer, said thick washer comprising two blind transverse holes, said hollow body of the further housing device comprising two markings to enable the insertion of corresponding mechanical fixing elements in the transverse holes so as to keep the thick washer in position. an upper, first housing device comprising: - a hollow body having a cylindrical extension between a first and a second end (2a, 2b) and comprising a bottom portion at said second end, said bottom portion having an opening towards the outside; - a hollow projection connected to said bottom portion so as to communicate with the opening and having an extension away from it; - a plurality of flaps arranged around the hollow body; - a hollow body having a cylindrical extension between a first and a second end (2a, 2b) and comprising a bottom portion at said second end, said bottom portion having an opening towards the outside; - a hollow projection connected to said bottom portion so as to communicate with the opening and having an extension away from it; - a plurality of flaps arranged around the hollow body; a first plate for sharing the compressive load arranged inside the hollow body of the first housing device, one side of said first plate being in contact with the bottom portion; a second plate for sharing the tensile load at an opposite side of the first plate with respect to the bottom portion; a nut interposed between the first and the second plate (11, 12); an extension tube having an end portion inserted into the hollow projection; a further housing device, a hollow projection of which is mounted at an opposite end of the extension tube, said fixing system comprising a screwing means from above of a connection bar arranged in the further housing device, wherein said screwing means from above comprises a thick washer and a threaded portion associated therewith for the screwing from above of the connection bar, wherein said threaded portion is made in a through hole of the thick washer, said thick washer comprising two blind transverse holes, said hollow body of the further housing device comprising two markings to enable the insertion of corresponding mechanical fixing elements in the transverse holes so as to keep the thick washer in position.