  In some models beyond the Standard Model where lepton number violation by two
units is forbidden (implying neutrinos cannot be Majorana fermions), violation
by four units can still occur, allowing neutrinoless quadruple beta decay. The
isotope 150-Nd is one of the very few isotopes where this process could be
experimentally observed. The experimental signature consists of four electrons
with a total energy equal to the Q-value of the decay. The NEMO-3 experiment in
the Modane Underground Laboratory in France ran from 2003 to 2011, and studied
seven isotopes of interest including 150-Nd. This article describes the result
of the first experimental search for neutrinoless quadruple beta decay using
the entire NEMO-3 data set for 36.5 g of 150-Nd with 5.25 years of data. No
evidence is found of this decay, and lower limits at the 90% CL on the
half-life are set in the range (1.1 - 3.2) $\times 10^{21}$ years
