本文给出了可分Ｈｉｌｂｅｒｔ空间上的二宽度ＣＳＬ代数分解成其对角与它的一个范数闭理想（即满足Ｒｉｎｇｒｏｓｅ条件的算子集）直和的充要条件是：此二宽度ＣＳＬ是由一个有限ＣＳＬ与一个有补ＣＳＬ生成的．

In this paper, we prove that the sufficient and necessary conditions for a width-two CSL algebra in a separable Hilbert space to be decomposed into the direct sum of the diagonal and its norm closed ideal (i.e. the set of operators set satisfying Ringrose condition): it is generated by a finite CSL and a complemented CSL.