  The two-photon ${1s}^{2} 2s 2p~^3\mbox{P}_0 \rightarrow {1s}^{2} {2s}^2$
$^1\mbox{S}_0$ transition in berylliumlike ions is theoretically investigated
within a full relativistic framework and a second-order perturbation theory. We
focus our analysis on how electron correlation, as well as the negative-energy
spectrum can affect the forbidden $E1M1$ decay rate. For this purpose we
include the electronic correlation by an effective potential and within an
active-electron model. Due to its experimental interest, evaluation of decay
rates are performed for berylliumlike xenon and uranium. We find that the
negative-energy contribution can be neglected in the present decay rate. On the
other hand, if contributions of electronic correlation are not carefully taken
into account, it may change the lifetime of the metastable state by 20\%. By
performing a full-relativistic $jj$-coupling calculation, we found
discrepancies for the decay rate of an order of 2 compared to non-relativistic
$LS$-coupling calculations, for the selected heavy ions.
