We introduce a NP-complete problem named RHC and prove its NP-complete property in this paper. Secondly，we discuss the complexity any algorithm solving RHC presents by counting the moving times of the tape head on turning machine. The conclution drawn from our analysis shows at least that it is difficult to find an algorithm to solve RHC though the analysis is not a mathematical one, Hence，maybe it needs only time we think，to confirm the analysis.