  Mass measurement of a particle whose decay products including invisible
particles is a challenging task at colliders. For a new physics model involving
a dark matter candidate $N$ and a $Z_2$ symmetry that stabilizes it, a typical
new process at $e^+e^-$ colliders is the pair production $e^+e^- \to Y\bar{Y}$
followed by decay processes $Y\to aN$ and $\bar{Y}\to b\bar{N}$, where $a$ and
$b$ are visible but $N$ is invisible. In this work, we propose a new method to
measure the physical masses in this topology by making use of the kinematic
equations given by momentum-energy conservation and on-shell conditions. For
each event, the solvability of these equations determines a limited region on
the trial $m_Y$-$m_N$ plane. The edge of this region can be used to define two
variables, $m_Y^\mathrm{edge}$ and $m_N^\mathrm{edge}$, whose distributions are
utilized to derive the measurement values of $m_Y$ and $m_N$. The measurement
deviations and uncertainties are also estimated after including detector
effects and background contamination.
