real analysis - There is a holomorphic and bijective function of $mathbb {D}$ in $mathbb{D}setminus(0,1]$?

There is a holomorphic and bijective function of $\mathbb{D}$ in $\mathbb{D}\setminus(0,1]$? where $\mathbb{D}$ denotes the open unit disk in the complex plane.

Idea: I really need to prove that there is a holomorphic and bijective function of $R={\{z\in\mathbb{C}: Re(z)>0 , Im(z)>0}\}$ in $\mathbb{D}\setminus(0,1]$ But just find a function with such properties of $\mathbb{D}$ in $\mathbb{D}\setminus(0,1]$, and then make the composition with the transformation of cayley and the function $f(z)=z^2$.

Thanks for the help!!