The deficiency of the triceps tendon has been considered a relative contraindication to performing a total elbow arthroplasty. One of the conditions that may compromise triceps integrity is the presence of an olecranon non-union (ON). In this scenario, the placement of a total elbow arthroplasty in a patient with end-stage elbow arthritis is a complex problem to be solved. The aim of this study is to describe the surgical technique for the placement of a TEA in the context of a previous ON and to report the results of three cases. Surgical technique: the focus of the nonunion is identified, and the olecranon fragment is proximally reflected with the triceps tendon to allow accurate exposure of the medullary canal of the ulna and easy access to the joint. With the elbow in a fully flexed position, the previously assembled test prosthesis is placed and the proximal ulna fragment should then be reduced to match the distal ulna. Osteosynthesis with a tension band technique was performed at 45° of elbow extension. A non-absorbable Krackow suture (Ti-Cron 2-0) from the triceps's tendon to the hole of the wire in the distal ulna is applied to decrease the triceps tension traction. Bone grafting is performed when a persistent gap is present at the fracture site following reduction. This technique enables us to achieve a stable elbow with little pain and maintains the extensor apparatus's continuity.