Various multistage interconnection networks have been proposed in the literature and utilized in commercial projects. But there exists a further scope of improvement and the need for new fault tolerant multistage interconnection networks, which can withstand multiple switch or link failures. Recently, design layouts of four disjoint paths gamma interconnection networks have been proposed and named as 4DGIN-1 and 4DGIN-2, respectively. These proposed design layouts of 4DGINs produce different number of alternative paths ranging from five to seven for different tag values. In this paper, a new variant, viz., 4DGIN-3 is introduced, which generates four disjoint paths similar to 4DGIN-1 and 4DGIN-2 but with a total of six number of alternative paths for every tag value. This feature of the proposed design, in turn, results in same reliability for each tag value at various assumed reliability of switching elements despite having the similar topology and hardware cost as that of the earlier 4DGINs. A comparison of the proposed design with the existing 4DGINs has also been provided in this paper.