  Magnetic clouds (MCs) are observed insitu by spacecraft. The rotation of
their magnetic field is typically interpreted as the crossing of a twisted
magnetic flux tube, or flux rope, which was launched from the solar corona. The
detailed magnetic measurements across MCs permit us to infer the flux rope
characteristics. Still, the precise spatial distribution of the magnetic twist
is challenging, and thus is debated. In order to improve the robustness of the
results, we performed a superposed epoch analysis (SEA) of a set of well
observed MCs at 1 au. While previous work was done using the MC central time,
we here used the result of a fitted flux rope model to select the time of the
closest approach to the flux rope axis. This implies a precise separation of
the in- and outbound regions to coherently phase the observed signals. We also
searched for and minimised the possible biases such as magnetic asymmetry and a
finite impact parameter. We applied the SEA to derive the median profiles both
for the flux rope remaining when crossed by the spacecraft and to recover the
one present before erosion. In particular, the median azimuthal B component is
nearly a linear function of the radius. More generally, the results confirm our
previous results realised without such a deep analysis. The twist profile is
nearly uniform in the flux rope core, with a steep increase at the border of
the flux rope and with similar profiles in the in- and outbound regions. The
main difference with our previous study is a larger twist by $\sim 20\%$.
