In an improved method for surgically treating a sleep-related breathing disorder, comprising hyoid distruction/expansion and hyo-mandibular suspension, an implant comprises a polypropylene and/or reticulated elastomeric biostable polyurethane matrix. The matrix is positioned between two or more segments of the distructed hyoid bone. A single or multiple midline or paramedian incisions are made under a patient's chin; soft tissues overlying the mandible are cleaned; a first screw is inserted into the edge of the mandible; a second screw is inserted into the inferior edge of the mandible; a second horizontal incision is made over the body of the hyoid; the infrahyoid muscles are separated from the body of the hyoid bone; the hyoid is refracted and stabilized; the sternohyoid and thyrohyoid muscles are detached from the body of the hyoid between the lesser cornuae; the hyoid bone is divided midline or paramedian into two or more segments; and an absorbable or nonabsorbable, rigid or semirigid, implant is positioned between segments of the hyoid bone. The hyoid bone is stabilized by the implant; and sutures or portions of polypropylene and/or polyurethane matrix are passed around the hyoid bone segments and implant to connect to muscle still attached to the upper portion of the hyoid bone, wherein the hypopharyngeal airway is expanded.