  We present new observations of four closely-spaced NUV transits of the hot
Jupiter-like exoplanet WASP-12b using HST/COS, significantly increasing the
phase resolution of the observed NUV light curve relative to previous
observations, while minimising the temporal variation of the system. We observe
significant excess NUV absorption during the transit, with mean normalised
in-transit fluxes of $F_\mathrm{norm}\simeq0.97$, i.e. $\simeq$2-5 $\sigma$
deeper than the optical transit level of $\simeq0.986$ for a uniform stellar
disk (the exact confidence level depending on the normalisation method used).
We further observe an asymmetric transit shape, such that the post-conjunction
fluxes are overall $\simeq$2-3 $\sigma$ higher than pre-conjunction values, and
characterised by rapid variations in count rate between the pre-conjunction and
out of transit levels. We do not find evidence for an early ingress to the NUV
transit as suggested by earlier HST observations. However, we show that the NUV
count rate observed prior to the optical transit is highly variable, but
overall $\simeq$2.2-3.0 $\sigma$ below the post-transit values and comparable
in depth to the optical transit, possibly forming a variable region of NUV
absorption from at least phase $\phi\simeq$0.83, limited by the data coverage.
