We detected four outbursts of V359 Cen (possible nova discovered in 1939) between 1999 and 2002. Time-resolved CCD photometry during two outbursts (1999 and 2002) revealed that V359 Cen is actually a long-period SU UMa-type dwarf nova with a mean superhump period of 0.08092(1) d. We identified its supercycle length as 307-397 d. This secure identification of the superhump period precludes the previously supposed possibility that V359 Cen could be related to a WZ Sge-type system with a long persistence of late superhumps. The outburst characteristics of V359 Cen are, however, rather unusual in its low occurrence of normal outbursts.
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