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The Catani--Seymour dipole subtraction is a general and powerful procedure tocalculate the QCD next-to-leading order corrections for collider observables.We clearly define a practical algorithm to use the dipole subtraction. Thealgorithm is called the Dipole splitting algorithm (DSA). The DSA is applied toan arbitrary process by following well defined steps. The subtraction termscreated by the DSA can be summarized in a compact form by tables. We present atemplate for the summary tables. One advantage of the DSA is to allow astraightforward algorithm to prove the consistency relation of all thesubtraction terms. The proof algorithm is presented in the subsequent article.We demonstrate the DSA in two collider processes, $pp \to \mu^{-}\mu^{+}$ and$2\,jets$. Further as a confirmation of the DSA it is shown that the analyticalresults obtained by the DSA at the Drell-Yan process exactly agree with thewell known results obtained by the traditional method.

Dipole Splitting Algorithm -- A practical algorithm to use the dipole subtraction procedure --