Biometric data cannot be changed or canceled if they are compromised. To cope with this problem, changeable biometric systems that use transformed biometric data instead of original data have recently been introduced. In this paper, we propose a changeable biometric system for face recognition that uses LNMF (Local Non-negative Matrix Factorization), or parts-based localized representation. Two different sets of LNMF bases can be computed from given training images when training them twice and two different LNMF feature vectors can then be extracted from an input face image using these LNMF bases. The two feature vectors are scrambled randomly and a new transformed feature vector can be generated by the addition of the two feature vectors. The scrambling rule is determined by a given user's PIN, and when the transformed feature vector is compromised, it is replaced by using a new scrambling rule. Because the transformed template is generated by the addition of two vectors, the two different original LNMF feature vectors cannot be recovered from the transformed feature vector. Experimental results show that the proposed method performs better than the PCA and original LNMF-based methods. Also the transformed feature vector satisfies the requirement of changeability.