The Extended QR-RLS algorithm is a computationally efficient square-root adaptive filtering algorithm for recursive least-squares (RLS) estimation. It is based upon QR decomposition. The motivation for using the QR decomposition in adaptive filtering is to exploit its good numerical properties. This method solves directly for the time-recursive least squares filter vector, while avoiding the highly serial back substitution Step required in direct QR approaches. This algorithm bears one to one correspondence that exists between the Kalman variables and the RLS variables.Furthermore, this method is based on Givens rotations that lend itself to a parallel implementation in the form of a systolic array. This method offers superior numerical properties. It is computationally efficient and highly concurrent. Parallel implementation of the resulting method in the form of systolic array and its application to system identification is briefly discussed.