  We investigate the period halving of persistent currents(PCs) of
non-interacting electrons in isolated mesoscopic M\"{o}bius ladders without
disorder, pierced by Aharonov-Bhom flux. The mechanisms of the period halving
effect depend on the parity of the number of electrons as well as on the
interchain hopping. Although the data of PCs in mesoscopic systems are
sample-specific, some simple rules are found in the canonical ensemble average,
such as all the odd harmonics of the PCs disappear, and the signals of even
harmonics are non-negative. {PACS number(s): 73.23.Ra, 73.23.-b, 68.65.-k}
