Fingerprint template security is essential to safeguard the templates from an attacker. There are existing methods to safeguard the templates but they involve storing the fingerprint itself. Hence to overcome that, a new fingerprint template security technique has been proposed in this paper by introducing a User Defined Graph called Random Ball Graph (RBG). Feature vector is extracted from the Left Fingerprint, Right Fingerprint and Palm Print during enrollment of fingerprints and combined. The captured information from the biometrics is stored in RBG where the insertion and traversal of feature vector are unknown to the attacker. So even if the database is stolen by the attacker, the sequence cannot be obtained. The security analysis shows that the system is highly secure and has a high computational hardness. The experimental results show an Equal Error Rate (EER) of 4.8%. Copyright © 2017 American Scientific Publishers.