A new tendon driven mechanism, embedded into a soft hand exoskeleton for rehabilitation and assistance, was proposed in this study. The proposed solution was a pulley flexion mechanism inspired by the human musculoskeletal system to enable a natural and comfortable finger flexion. A biomechanical constraint for the finger flexion motion states that the relation between the proximal interphalangeal joint angle of the finger should always be flexed around 1.5 times the distal interphalangeal joint angle. The study aimed to comply with this constraint, by simultaneously distributing the forces over the distal and middle finger phalanges. For evaluation, the voluntary and exoskeleton flexions were compared based on the relation between the proximal and distal interphalangeal joint angles. The results showed that during the exoskeleton flexion the relation between the interphalangeal joints complied with the biomechanical constraint, where the proximal interphalangeal joint angle was 1.5 times larger than the distal interphalangeal joint. This ensures that the mechanism flexes the finger comfortably. The proposed solution is therefore a promising design for a novel soft exoskeleton that will be used for training and assistance of patients with hand paralysis.