  Neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay is related to many
fundamental concepts in nuclear and particle physics beyond the standard model.
Currently there are many experiments searching for this weak process. An
accurate knowledge of the nuclear matrix element for the $0\nu\beta\beta$ decay
is essential for determining the effective neutrino mass once this process is
eventually measured. We report the first full relativistic description of the
$0\nu\beta\beta$ decay matrix element based on a state-of-the-art nuclear
structure model. We adopt the full relativistic transition operators which are
derived with the charge-changing nucleonic currents composed of the vector
coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism
coupling terms. The wave functions for the initial and final nuclei are
determined by the multireference covariant density functional theory (MR-CDFT)
based on the point-coupling functional PC-PK1. The low-energy spectra and
electric quadrupole transitions in ${}^{150}$Nd and its daughter nucleus
${}^{150}$Sm are well reproduced by the MR-CDFT calculations. The
$0\nu\beta\beta$ decay matrix elements for both the $0_1^+\rightarrow 0_1^+$
and $0_1^+\rightarrow 0_2^+$ decays of ${}^{150}$Nd are evaluated. The effects
of particle number projection, static and dynamic deformations, and the full
relativistic structure of the transition operators on the matrix elements are
studied in detail. The resulting $0\nu\beta\beta$ decay matrix element for the
$0_1^+\rightarrow 0_1^+$ transition is $5.60$, which gives the most optimistic
prediction for the next generation of experiments searching for the
$0\nu\beta\beta$ decay in ${}^{150}$Nd.
