A new adaptive filtering algorithm for time-series data based on the QRD inverse-updates method of Pan and Plemmons is derived from first principles. In common with other fast algorithms for time-series adaptive filtering, this algorithm only requires O(p) operations for the solution of a pth-order problem. Unlike previous fast algorithms based on the QRD technique, the algorithm presented here explicitly produces the transversal filter weights. Furthermore the derivation of the algorithm is achieved, quite simply, by means of signal-flow-graph manipulation. The relationship between this fast QRD inverse-updates algorithm and the FTF algorithm is briefly discussed. The results of some preliminary computer simulations of the algorithm, using finite-precision floating-point arithmetic, are presented.