A logic of conditionals with primary-condition and secondary-condition C2Lm is constructed in Liu Zhuang-hu and Li Xiao-wu(See Bibliography[1]).This paper studies the problem concerning redundant conditions in logic of conditionals with primary-condition and secondary-condition on the basis of that system.It proves C2Lm cannot be extended in one of the ways suggested by See Bibliography[1].Then,this paper constructs system C1 characterizing some redundant condition and proves its syntactic and semantic properties.