In this paper a modified version of the standard least-squares algorithm is presented. The aim is to use the proposed modified LS algorithm in linear time-varying systems. The proposed modification involves the addition of extra terms to both the parameter estimates' and the covariance's update laws. We establish a series of properties on the identification error, the parameter estimates and the covariance matrix. These properties are important in an adaptive control context, because LS algorithms provide an easy way of modifying the parameter estimates in order to avoid singular points in the control scheme.