In this paper, we propose a bifurcation-based descriptor using a local structure of blood vessel features on sclera for identity verification. The sclera, one of the ocular biometric traits, can be defined as the white and opaque region of the eye. Unlike iris patterns shown in the near infrared light, the blood vessel patterns of the region can be captured in visible light. As the variability of vessel thickness is not stable, morphological operations are applied to make the vessels thin. Then, bifurcations are extracted on the vessels, and a local structure is constructed of the distances and the angles between a central bifurcation and its neighbors. Finally, each local structure from template and query images is matched considering the topological relation, whereas the traditional methods consider matching features globally. The experimental results using public database, UBIRIS.v1, show a superior equal error rate of 1.92% compared to the existing methods.