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Context: The $^{15}$N fractionation has been observed to show largevariations among astrophysical sources, depending both on the type of targetand on the molecular tracer used. These variations cannot be reproduced by thecurrent chemical models.  Aims: Until now, the $^{14}$N/$^{15}$N ratio in N$_2$H$^+$ has beenaccurately measured in only one prestellar source, L1544, where strong levelsof 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 fideprestellar 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 anon-local radiative transfer code in order to obtain accurate estimates of themolecular column densities, including the one for the optically thickN$_2$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 $630-770$ andsignificantly differ with the value, predicted by the most recent chemicalmodels, of $\approx 440$, close to the protosolar value. Our prestellar coresample shows high level of depletion of $^{15}$N in diazenylium, as previouslyfound in L1544. A revision of the N chemical networks is needed in order toexplain these results.

$^{14}$N/$^{15}$N ratio measurements in prestellar cores with N$_2$H$^+$: new evidence of $^{15}$N-antifractionation