  The neutrinoless double-beta ($0\nu\beta\beta$) decay is a unique process to
identify the Majorana nature of massive neutrinos, and its rate depends on the
size of the effective Majorana neutrino mass $\langle m\rangle_{ee}$. We put
forward a novel "coupling-rod" diagram to describe $\langle m\rangle_{ee}$ in
the complex plane, by which the effects of the neutrino mass ordering and
CP-violating phases on $\langle m\rangle_{ee}$ are intuitively understood. We
show that this geometric language allows us to easily obtain the maximum and
minimum of $|\langle m\rangle_{ee}|$. It remains usable even if there is a kind
of new physics contributing to $\langle m\rangle_{ee}$, and it can also be
extended to describe the effective Majorana masses $\langle m\rangle_{e\mu}$,
$\langle m\rangle_{e\tau}$, $\langle m\rangle_{\mu\mu}$, $\langle
m\rangle_{\mu\tau}$ and $\langle m\rangle_{\tau\tau}$ which may appear in some
other lepton-number-violating processes.
