The Vector Random Decrement technique has been developed as an efficient method for transforming ambient responses into free decays of linear structures. It is shown that the VRD functions nay contain as much information about the modes as the really measured free decay responses. In this paper, the theory of the VRD technique is extended by applying the concept of the mode shape ratio into the Ibrahim Time Domain modal parameter identification algorithm. The VRD function is not shifted in the correction procedures for constant time shifts of the proposed VRD technique. Thus, a number of points equal to the largest of the time shifts used in the vector triggering condition are not deleted. In the VRD functions, any influence of the input to the system is averaged out. The proposed technique is compared with the traditional VRD technique by assessment of the modal parameters. The applicability of the VRD technique has been justified through a simulation study and a study of the response of a laboratory beam model subject to ambient loads.