This paper is a continuation of RZhMat 1981, 7A438. Suppose R is a commutative ring generated by its group of units R^* and there exist[Figure not available: see fulltext.] such that[Figure not available: see fulltext.]. Suppose also that ℑ is the Jacobson radical of R, and B(ℑ) is a subgroup of GL(n,R) consisting of the matrices a=(a_ij) such that a_ij∃ℑ for i>j. If a matrix a∃B(ℑ) is represented in the form a=udv, where u is upper unitriangular, d is diagonal, and v is lower unitriangular, then u,v∃〈D,aDa^-1〉, where D=D(n,R) is the group of diagonal matrices. In particular, D is abnormal in B(ℑ)