As security and reliability issues grow to be major social concerns, there are growing interests in combining multiple Global Navigation Satellite Systems (GNSS) into new generation of GNSS. Consequently traditional integrity monitoring systems like Receiver Autonomous Integrity Monitoring (RAIM) techniques which are generally based on the assumption of a single outlier model, will not perform well for the new GNSS. In this paper an improved RAIM scheme based on Least Squares residuals is presented with considerations on high availability of satellites, multiple outliers, fault detection and isolation. While existing RAIM algorithms generally identify one outlier in each iteration of computation, the new scheme is able to identify two outliers in each iteration. This new method also takes into account the joint impacts of multiple outliers on good measurements and the correlation between two measurements. Detailed simulations and analysis have been carried out to assess the new scheme performance to compare against the traditional RAIM algorithm based on Least Squares. Results show that the scheme is well capable of identifying multiple outliers without affecting the navigation solution.