This study investigates a new \emph{client-dependent normalisation} to improve biometric authentication systems. There exists many client-de-pendent score normalisation techniques applied to speaker authentication, such as Z-Norm, D-Norm and T-Norm. Such normalisation is intended to adjust the variation across different client models. We propose ``F-ratio'' normalisation, or F-Norm, applied to face and speaker authentication systems. This normalisation requires only that \emph{as few as} two client-dependent accesses are available (the more the better). Different from previous normalisation techniques, F-Norm considers the client and impostor distributions \emph{simultaneously}. We show that F-ratio is a natural choice because it is directly associated to Equal Error Rate. It has the effect of centering the client and impostor distributions such that a global threshold can be easily found. Another difference is that F-Norm actually ``interpolates'' between client-independent and client-dependent information by introducing a mixture parameter. This parameter \emph{can be optimised} to maximise the class dispersion (the degree of separability between client and impostor distributions) while the aforementioned normalisation techniques cannot. unimodal experiments XM2VTS multimodal database show that such normalisation is advantageous over Z-Norm, client-dependent threshold normalisation or no normalisation.