Hyperbolic component W of the Mandelbrot set M is a component of its interior, such that, for c in W, the quadratic polynomial f_c(z)=z²+c has an attracting periodic orbit. One of the fundamental facts about the set M is a theorem by Douady, Hubbard and Sullivan, which states that the multiplier of this attracting orbit performs a conformal isomorphism of the component W onto the unit disk. We prove an extension of this result. It has few interesting applications to the problem of geometry of the Mandelbrot and Julia sets.