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In the present paper a new scheme is presented which combines the Sequential Function Specification and the Dual Reciprocity Boundary Element Methods. In this scheme the unknown boundary condition is estimated sequentially by using two transformation matrices. The matrices defined in the direct heat conduction calculations by the Dual Reciprocity Boundary Element Method are used as a basis for the definition of the transformation matrices, and the mathematical derivations for the inverse estimation are in accordance with the Sequential Function Specification of Beck. In order to compare the speed and the accuracy of the method with the existing Sequential Function Specification Method, the exact analytical solution of a simulated test case is utilized. Results indicate an impressive improvement in the efficiency as well as the accuracy of this scheme as compared with the conventional ones. The results are accurate and stable foe error amplitudes up to one percent of measured temperatures.