This paper presents a new approach to authenticate individuals using triangulation of hand vein images and simultaneous extraction of knuckle shape information. The proposed method is fully automated and employs palm dorsal hand vein images acquired from the low-cost, near infrared, contactless imaging. The knuckle tips are used as key points for the image normalization and extraction of region of interest. The matching scores are generated in two parallel stages: (i) hierarchical matching score from the four topologies of triangulation in the binarized vein structures and (ii) from the geometrical features consisting of knuckle point perimeter distances in the acquired images. The weighted score level combination from these two matching scores are used to authenticate the individuals. The achieved experimental results from the proposed system using contactless palm dorsal-hand vein images are promising (equal error rate of 1.14%) and suggest more user friendly alternative for user identification.