Two$-$Way DFA$$s

Let M be a $2-$way DFA with alphabet $\backslash$Sigma $.$ Then there exists another $2-$way DFA M$$ such that L$($M$)$ and L$($M$)$ are disjoint, and the union of L$($M$)$ and L$($M$)$ is $\backslash$Sigma $*.$ True or false