  We show that using either the method of Page & Carrera or the well-known
$1/V_a$ method to construct the binned luminosity function (LF) of a flux
limited sample of Active Galactic Nuclei (AGN) can produce an artificial
flattening (or steepening in the case of negative evolution) of the binned LF
for bins intersected by the flux cutoff of the sample. This effect is more
pronounced for samples with steep and strongly evolving parent LFs but is still
present even for non-evolving LFs. As a result of this distortion of the true
LF, fitting a model LF to binned data may lead to errors in the estimation of
the parameters and may even prompt the erroneous use of broken power law
functions. We compute the expected positions of apparent breaks in the binned
LF. We show that these spurious breaks in the binned LFs can be avoided if the
binning is done in the flux--redshift plane instead of the typically used
luminosity--redshift plane. Binning in the flux--redshift plane can be used in
conjunction with the binning in the luminosity--redshift plane to test for real
breaks in the binned LFs and to identify the features that are the result of
binning biases. We illustrate this effect for most typical forms of luminosity
dependence and redshift evolution and show how the proposed method helps
address this problem. We also apply this method to the MOJAVE AGN sample and
show that it eliminates an apparent break in the binned LF.
