This paper presents a new method for addressing the challenging problem of generating changeable and privacy preserving templates for face based biometric verification systems. The proposed method transforms the extracted face feature vector by a random orthonormal matrix, and the sorted index numbers of the resulting feature vector in the transformed domain is stored as template for verification. A new matching algorithm is introduced for measuring the similarity between the template and the authenticating image. Two different application scenarios, user-independent and user-dependent transformations are discussed. A vector translation technique is introduced to enhance the changeability of the generated templates. Experimental results on a large face data set demonstrate that the proposed method may improve the verification performance, produce strong changeability, and protect the user's privacy.