This　paper　is　concerned　with　the　assumptions　in　the　convergence　theorem　of　the　nonlinear　ABS　algorithm.　In　the　published　papers,　it　has　been　assumed　that　the　condition　number　of　the　scaling　matrices　is　uniformly　bounded　above.　In　this　paper　it　is　shown　that　the　above　condition　can　be　replaced　by　the　following　simpler　condition:　the　orthogonality　measure　of　scaling　vector　sets　is　uniformly　bounded　from　below.　It　is　also　shown　that　the　latter　condition　is　weaker　than　the　original　one.　©　1991　Instituto　di　Elaborazione　della　Informazione　del　CNR.