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A method for adaptive linear estimation is proposed based on a Time Domain Orthogonality condition. This algorithm arises naturally from the criterion used rather than through the application of a numerical analysis method as in the derivation of the LMS Gradient Algorithm. However, in addition to being a new and potentially useful algorithm, the resulting recursive method is suprisingly similar to the LMS Gradient Algorithm. With the addition of certain simplifying assumptions, the TDO algorithm reduces to the LPIS Gradient Algorithm except that a data dependent term replaces the constant parameter µ found In the LMS Gradient Method. In fact, it is shown that this data dependent term is an estimate of the optimum µ for maximum rate of convergence.