This paper presents a real-time Consistent Mono-cular EKF-SLAM process. We introduce the notion of bias which allows to model the natural drift of the SLAM process. Thanks to it , the consistency of the filter is guaranteed. By connecting the bias to the different landmarks and to the vehicle pose , the estimates become tightly bound to the SLAM drift. It means that a loop closure , for instance , will naturally estimate the bias and so correct the vehicle pose and landmark positions without any special processing. We developed a dedicated architecture in order to integrate the bias. It uses an Extended Kalman Filter and has the advantage to be totally decorrelated from the classical SLAM process. Thanks to it , any algorithm , with any kind of sensors or methods , can be used instead of the monocular SLAM employed in this paper , as long as it produces landmark estimates and their uncertainty. This approach was validated with a real experiment composed of a long loop .