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Our previous work on combining switches multistage interconnection network (CSMIN) makes use of distance tag routing algorithm to provide two correct disjoint paths for every source-destination pair. Our algorithm backtracks a packet to the previous stage and takes the other disjoint path in the event of a fault or a collision in the network. To eliminate the backtracking penalties of CSMIN, we propose a new design called fully-chained combining switches multistage interconnection network (FCSMIN). FCSMIN has the similar characteristics of 1-fault tolerance and two disjoint paths between any source-destination pair but it can tolerate at least one link or switch fault at each stage without backtracking. Our comparative analysis and results show that FCSMIN has the added advantages of destination tag routing, lower hardware costs than CSMIN, strong reroutability and lower pre-processing overhead.