  Computing polarised intensities from noisy data in Stokes U and Q suffers
from a positive bias that should be suppressed. To develop a correction method
that, when applied to maps, should provide a distribution of polarised
intensity that closely follows the signal from the source. We propose a new
method to suppress the bias by estimating the polarisation angle of the source
signal in a noisy environment with help of a modified median filter. We then
determine the polarised intensity, including the noise, by projection of the
observed values of Stokes U and Q onto the direction of this polarisation
angle. We show that our new method represents the true signal very well. If the
noise distribution in the maps of U and Q is Gaussian, then in the corrected
map of polarised intensity it is also Gaussian. Smoothing to larger Gaussian
beamsizes, to improve the signal-to-noise ratio, can be done directly with our
method in the map of the polarised intensity. Our method also works in case of
non-Gaussian noise distributions. The maps of the corrected polarised
intensities and polarisation angles are reliable even in regions with weak
signals and provide integrated flux densities and degrees of polarisation
without the cumulative effect of the bias, which especially affects faint
sources. Features at low intensity levels like 'depolarisation canals' are
smoother than in the maps using the previous methods, which has broader
implications, for example on the interpretation of interstellar turbulence.
