  In this paper, we investigate new sufficient conditions to ensure the
existence of a unique global strong solution of stochastic differential
equations with jumps. By using Euler approximation and by utilising a new test
function $\varphi_\delta$ (see the following definition (\ref{pntas1})), we
prove that there is a unique global strong solution for the initial value
problem of the equation. The condition we posed is even weaker than the local
Lipschitzian continuity of the coefficients. We also present an example to show
that our conditions are indeed weaker than those relevant conditions existing
in the literature.
