  We analyzed Asteroid Terrestrial-impact Last Alert System (ATLAS), Zwicky
Transient Facility (ZTF) and All-Sky Automated Survey for Supernovae (ASAS-SN)
data of MASTER OT J055845.55+391533.4 and found that this object repeats
superoutburst with a dip in the middle of the outburst followed by long and
sometimes oscillating rebrightening, just like a WZ Sge-type dwarf nova or an
AM CVn-type object. The mean supercycle was 298(8) d, too short for a WZ Sge
star, but with only a few normal outbursts. We also observed the 2023
February-March superoutburst and established the superhump period of 0.05509(2)
d. This period appears to exclude the possibility of an AM CVn star. Although
the 2023 observations could not detect superhumps after the dip, the 2014, 2016
and 2021 data seem to suggest that low-amplitude superhumps were present during
the rebrightening phase. We note that a dip during a superoutburst is a feature
common to the unusual SU UMa-type dwarf nova MASTER OT J172758.09+380021.5
during some of its superoutbursts. These objects may comprise a new class of
rebrightening phenomenon in SU UMa-type dwarf novae.
