  We examine a new mechanism of $e^+e^-$ pair production in $NN$ collisions
associated with the $NN$-decoupled dibaryon $d^\star_1$(1956) formation in the
process $NN \to \gamma^\star d^\star_1$, where $\gamma^\star$ is the virtual
photon which converts into a $e^+e^-$ pair. It is shown that a substantial
excess of dielectron yields from $Ca+Ca$ and $C+C$ collisions at 1 GeV/A in the
dielectron mass spectra in the region from 0.2 to 0.5 GeV/$c^2$ measured by the
\textit{DLS Collaboration} as compared with calculated ones can be attributed
to the contribution of this mechanism. A simple means for verification of the
existence of such a mechanism is proposed.
