Classical irregular scattering and fluctuation of quantum transition probability

S-matrix of a collision system exhibiting classical irregular scattering is analyzed on the basis of the classical S-matrix theory. The S-matrix is represented as an infinite series, each term of which possesses a random phase factor. Each S-matrix element, in consequence, performs random walk on the complex plane when one varies the final state. Probability distribution of the S-matrix elements is derived theoretically.