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We show the derivation of the self-duality relation of abelian higher-formgauge field strength in the topologically nontrivial spacetime background. Theso-called Pasti-Sorokin-Tonin action for the self-dual abelian gauge fieldassumes that the spacetime topology is trivial to derive the self-dualityrelation using a gauge transformation of the action. In this paper we find anew gauge transformation of the same theory and show that this new gaugetransformation enables us to derive the self-duality relation even in thetopologically nontrivial spacetime background.

Note on the self-duality of gauge fields in topologically nontrivial spacetime