Abstract: A safety net assembly (16) includes elongated rigid attachment spars (34) having attachment-spar swivel links (36) which are selectively linked to an external net support (18) at first ends thereof but which further include traction-force-responsive clamp hooks (42) at second ends thereof for selectively gripping a lower flange (58) of a steel beam (12) located adjacent an exterior of a building (10). The safety net further includes pulleys, of winches (60) for example, mountable on extra attachment spars for lifting and lowering the external net support. The elongated rigid attachment spars are disengaged from the external net support and the external net support is attached to the extra attachment spars at a new vertical location. A truss structure (66) couples adjacent lateral net support spars (22) at unit ends. Corner net units are included.