提出了一条设计直线参数化方式的新标准——递归性标准，它和作者在“Ｔｈｒｅｅｃｏｎｄｉ－ｔｉｏｎｓｏｆａｇｏｏｄｌｉｎｅｐａｒａｍｅｔｅｒｉｚａｔｉｏｎ”文中提出的唯一性、有界性、均匀性三条标准一起构成了评价直线参数化方式优劣的新框架．根据上述四条标准，证明了不存在同时满足这四条标准的直线参数化方式和直线参数化方式ｃ＝αｘ＋（α０－｜α｜）ｙ，α∈［－α０，α０）不但满足唯一性、有界性和递归性标准，而且可以获得均匀性标准的最优近似． A new criterion of linear parameterization was proposed, which is recursive criterion. The three criteria of uniqueness, boundedness and homogeneity proposed by author in the article “Three condiments of agoodline parameterization” New frame. According to the above four criteria, it is proved that there exists no linear parameterization method and linear parameterization method c = αx + (α0- | α |) y, α∈ [-α0, α0) satisfying the four criteria at the same time. Boundary and recursive criteria, and can obtain the best approximation of the uniformity criterion.