  Context: The $^{15}$N fractionation has been observed to show large
variations among astrophysical sources, depending both on the type of target
and on the molecular tracer used. These variations cannot be reproduced by the
current chemical models.
  Aims: Until now, the $^{14}$N/$^{15}$N ratio in N$_2$H$^+$ has been
accurately measured in only one prestellar source, L1544, where strong levels
of fractionation, with depletion in $^{15}$N, are found ($^{14}$N/$^{15}$N$\:
\approx 1000$). In this paper we extend the sample to three more bona fide
prestellar cores, in order to understand if the antifractionation in N$_2$H$^+$
is a common feature of this kind of sources.
  Methods: We observed N$_2$H$^+$,N$^{15}$NH$^+$ and $^{15}$NNH$^+$ in L183,
L429 and L694-2 with the IRAM 30m telescope. We modeled the emission with a
non-local radiative transfer code in order to obtain accurate estimates of the
molecular column densities, including the one for the optically thick
N$_2$H$^+$. We used the most recent collisional rate coefficients available,
and with these we also re-analysed the L1544 spectra previously published.
  Results: The obtained isotopic ratios are in the range $630-770$ and
significantly differ with the value, predicted by the most recent chemical
models, of $\approx 440$, close to the protosolar value. Our prestellar core
sample shows high level of depletion of $^{15}$N in diazenylium, as previously
found in L1544. A revision of the N chemical networks is needed in order to
explain these results.
