This paper presents a novel approach for evaluating the decentralized closed-loop integrity (DCLI) of multivariable control systems. Through application of the left-right factorization to the decomposed relative interaction array, the relative interaction to a particular loop from other loops is represented by element summation of the decomposed relative interaction sequence. The maximum interactions from other loops under different combinations and sequences are determined by the maximum values of the decomposed relative interaction sequence according to the failure index. Consequently, the necessary and sufficient conditions for the DCLI of an individual loop under both single- and multiple-loop failure are provided. Also, a simple and effective algorithm for verifying the DCLI for multivariable processes is developed. The usefulness of the proposed approach is illustrated by two classical examples.