A new type of dominance measure based on triangular factorizations is developed and is named theL-dominancemeasure. This new measure is tighter than any existing dominance measures and in particular is tighter than those based on generalized dominance andM-matrix theory. TheL-dominance condition on matrices with non-positive off-diagonal elements is proved to be equivalent to theM-matrix condition. But in contrast to theM-matrix condition, the testing of theL-dominance condition is easier and can be carried out in sequential order. Furthermore, these special properties enable us to construct a synthesis based design procedure superior to those based on generalized dominance orM-matrix theory; the last two methods are generally regarded as post-mortem analytical tools only.