We investigate the process of photon splitting \gamma \to \gamma \gamma both below and above the pair-creation threshold in a strong magnetic field. We show that the limit of the collinear kinematics which is usually used in literature is inadequate in the strong magnetic field. It is caused by essential deviation of photon dispersion law from vacuum one. We also point out the necessity to take into account the large radiative corrections near the cyclotron resonances. The absorption coefficients for different channels are calculated. The process of electroÔ-positron pair creation due to photon splitting \gamma \to \gamma (\gamma^* \to e⁺e^-) is studied in the high energy limit of the initial photon. It is shown that this reaction dominate over tree process \gamma \to \gamma e⁺e^-. The possible astrophysical applications are discussed.

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