$\phi$ is called a Rudin's (orthogonal) function if $\phi$ is a function in $H^\infty$ and the different nonnegative powers of $\phi$ are orthogonal in $H^2$. When $\phi$ is a multiple of an inner function and $\phi(0) = 0,~\phi$ is a Rudin's function. Sundberg and Bishop showed that a Rudin's function is not necessarily a multiple of an inner function. We study a Rudin's function which is a linear combination of two inner functions or a polynomial of an inner function.