Personal authentication systems based on biometrics have given rise to new problems and challenges related to the protection of personal data, issues of less concern in traditional authentication systems. The irrevocability of biometric templates makes biometric systems very vulnerable to several attacks. In this paper we present a new approach for biometric template protection. Our objective is to build a non-invertible transformation, based on random projection, which meets the requirements of revocability, diversity, security and performance. In this context, we use the chaotic behavior of logistic map to build the projection vectors using a methodology that makes the construction of the projection matrix depend on the biometric template and its identity. The proposed approach has been evaluated and compared with Biohashing and BioPhasor using a rigorous security analysis. Our extensive experimental results using several databases (e.g., face, finger-knuckle and iris), show that the proposed technique has the ability to preserve and increase the performance of protected systems. Moreover, it is demonstrated that the security of the proposed approach is sufficiently robust to possible attacks keeping an acceptable balance between discrimination, diversity and non-invertibility.