A new computationally efficient algorithm for re- cursive least squares filtering is derived, which is based upon an inverse QR decomposition. The method solves directly for the time-recursive least squares filter vector, while avoiding the highly serial backsubstitution step required in previously de- rived direct QR approaches. Furthermore, the method employs orthogonal rotation operations to recursively update the filter, and thus preserves the inherent stability properties of QR ap- proaches to recursive least squares filtering. The results of sim- ulations over extremely long data sets are also presented, which suggest stability of the new time-recursive algorithm. Finally, parallel implementation of the resulting method is briefly dis- cussed, and computational wavefronts are displayed.