A suture needle construct for extracapsular ligament reconstruction in mammals. In a technique for using the suture needle construct of the invention, the joint is first explored, and the damaged ligament and meniscus are debrided. The joint capsule is closed and a tunnel is created at the appropriate location in the proximal tibia for tibial fixation. Subsequent to the formation of the tibial tunnel, the suture needle construct, i.e., a suture with a substantially curved needle at one end and a substantially straight needle at the other end, is brought in the proximity of the joint. The suture is passed around the lateral fabella using the substantially curved needle, then deep to the patellar ligament using the substantially straight needle, and through the tibial tunnel using the substantially straight needle. The needles are cut off, and the sutures are tensioned over the repair site.