A surgical sagittal saw blade assembly (22, 210, 260, 330, 350, 360) that is removably attachable to and actuatable by a handpiece, said blade assembly including: an elongated guide bar (110, 212, 262, 362), the guide bar having a proximal end and a thickness, and being formed with a feature (134, 136, 232, 236) for cooperating with features on the handpiece so as to releasably hold the guide bar to the handpiece; and a saw blade (112, 214, 288, 306, 330, 350, 366), the saw blade having: a base (162, 162a, 238, 290, 368) that is moveably mounted to the guide bar forward of the proximal end to oscillate around a point on the guide bar; and a head (166, 166a, 240, 294, 332, 372) formed with teeth (168, 168a, 295, 308, 334, 373) that extends from the base outside of the guide bar, characterized by: the saw blade head having a thickness at least as equal to the thickness of the guide bar, wherein the thicknesses are transversal to the oscillation plane of the blade and are further transversal to the elongated direction of the guide bar; and a pair of connecting members (114, 216, 296, 312, 344, 378), each connecting member having a first end connected to the saw blade base and a second end located adjacent the proximal end of the guide bar, said connecting members being located on opposed sides of the point around which the saw blade base oscillates, the second ends of the connecting members adapted for being coupled with a drive member integral with the handpiece, the connecting members configured for simultaneous reciprocation by the handpiece drive member in opposed reciprocation so that, as a result of the reciprocation, said connecting members pivot the saw head. an elongated guide bar (110, 212, 262, 362), the guide bar having a proximal end and a thickness, and being formed with a feature (134, 136, 232, 236) for cooperating with features on the handpiece so as to releasably hold the guide bar to the handpiece; and a saw blade (112, 214, 288, 306, 330, 350, 366), the saw blade having: a base (162, 162a, 238, 290, 368) that is moveably mounted to the guide bar forward of the proximal end to oscillate around a point on the guide bar; and a head (166, 166a, 240, 294, 332, 372) formed with teeth (168, 168a, 295, 308, 334, 373) that extends from the base outside of the guide bar, the saw blade head having a thickness at least as equal to the thickness of the guide bar, wherein the thicknesses are transversal to the oscillation plane of the blade and are further transversal to the elongated direction of the guide bar; and a pair of connecting members (114, 216, 296, 312, 344, 378), each connecting member having a first end connected to the saw blade base and a second end located adjacent the proximal end of the guide bar, said connecting members being located on opposed sides of the point around which the saw blade base oscillates, the second ends of the connecting members adapted for being coupled with a drive member integral with the handpiece, the connecting members configured for simultaneous reciprocation by the handpiece drive member in opposed reciprocation so that, as a result of the reciprocation, said connecting members pivot the saw head.