How do I find a holomorphic function that maps $z \in C : Re(z) > 0$ to $z \in C : Re(z) > 0$ $z\notin [0,1].$

Question

How do I find a holomorphic function that maps $z \in C : Re(z) > 0$ to $z \in C : Re(z) > 0$ $z\notin [0,1].$

I know that I have to use the reverse Cayley transform to work with the unit disk. I don't know exactly what I should do after that. I tried searching online for "commonly used" Möbius transforms that can maybe help me, but didn't find anything. Any help would be appreciated!