AbstractAdaptive algorithms are required in order to resolve the problems involved in improving the convergent property and reducing the number of multiplications per sample time. This paper presents an adaptive algorithm that can solve these problems: an algorithm in which a parameter called overlap-length that is based on orthogonal projection onto multidimensional space. This parameter can be set in compliance with the priorities of the above mentioned problems and can realize various execution forms, including conventional algorithms. With this parameter, this algorithm can reduce the number of multiplications per sample time, though it may cause a small drop in convergent property in comparison to conventional orthogonal projection algorithms.