We deduce a new formula for the perihelion advance $\Theta$ of a test particle in the Schwarzschild black hole by applying a newly developed nonlinear transformation within the Schwarzschild space-time. By this transformation we are able to apply the well-known formula valid in the weak-field approximation near infinity also to trajectories in the strong-field regime near the horizon of the black hole. The resulting formula has the structure $\Theta =c_1-c_2\ln (c_3^2-e^2)$ with positive constants $c_{1,2,3}$ depending on the angular momentum of the test particle. It is especially useful for orbits with large eccentricities $e<c_3<1$ showing that $\Theta \to \infty$ as $e\to c_3$.

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