In this paper for a given set of real interval numbers σ that has one positive interval number and nonnegative summation, we find an interval nonnegative matrix CI such that for each point set δ of given interval spectrum σ, there exists a point matrix C of CI such that δ is its spectrum. For this purpose, we use unit lower triangular matrices and specially try to use binary unit lower triangular matrices. We also study some conditions for existence solution of the problem
