Abstract: Due to the regular in structure and easy division of binary recursive network (BR network), it is a popular network structure in theoretical research and practical application. This paper first surveys the (strong) diagnosability, conditional diagnosability, g-good-neighbor conditional diagnosability, g-extra conditional diagnosability, diagnosis algorithms and binary recursive network. Then on the random multi-fault mode that the binary recursive network's failure nodes are greater than its connectivity, this paper proposes the theory and method of random multi-fault diagnosis analysis for BR network, including multi-fault conditional diagnosis analysis, multi-fault conditional diagnosis strategy construction, and multi-fault conditional diagnosis algorithm design.