The dimuon production mass spectrum has been measured with a beam of 4-20-GeV/c ${K}_{L}^{0}'\mathrm{s}$ incident on a copper target. The production of ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pairs resulting from the decay of vector mesons ($\ensuremath{\rho}, \ensuremath{\omega} \mathrm{and} \ensuremath{\varphi}$) was observed with a cross section of 55 \ifmmode\pm\else\textpm\fi{} 10 nb per nucleon for ${x}_{F}g0.25$ based on a specific production model. In addition we measured upper limits for ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ pair production cross sections with ${x}_{F}g0.25$ of 20 nb per nucleon for ${m}_{\ensuremath{\mu}\ensuremath{\mu}}l0.5$ GeV/${\mathit{c}}^{2}$ and 35 nb per nucleon at the $\ensuremath{\psi}(3100)$.