  Adding right-handed neutrinos to the Standard Model is a natural and simple
extension and is well motivated on both the theoretical and the experimental
side. We extend the Standard Model by adding only one right-handed Majorana
neutrino and study the sensitivity of the Near Detector of the DUNE experiment
to the new physics parameters, namely the mixing parameters $|U_{e 4}|^2$ and
$|U_{\mu 4}|^2$ and the mass $m_N$. The study relies on searches of the
products of right-handed neutrino decays, which is possible thanks to an
extremely intense beam and a state-of-the-art detection technology. This type
of direct test is carried out with very few assumptions and in an
almost-completely model-independent way, providing thus a strong result. A
background analysis is also performed, simulating the detector performance to
particle identification. It is found that the existing bounds in the MeV-range
can be improved by one order of magnitude in different detection channels.
