  We apply the complex analysis over the double numbers $D$ to study the
minimal time-like surfaces in $R^4_2$. A minimal time-like surface which is
free of degenerate points is said to be of general type. We divide the minimal
time-like surfaces of general type into three types and prove that these
surfaces admit special geometric (canonical) parameters. Then the geometry of
the minimal time-like surfaces of general type is determined by the Gauss
curvature $K$ and the curvature of the normal connection $\varkappa$,
satisfying the system of natural equations for these surfaces. We prove the
following: If $(K, \varkappa), \, K^2- \varkappa^2 > 0 $ is a solution to the
system of natural equations, then there exists exactly one minimal time-like
surface of the first type and exactly one minimal time-like surface of the
second type with invariants $(K, \varkappa)$; if $(K, \varkappa),\, K^2-
\varkappa^2 < 0 $ is a solution to the system of natural equations, then there
exists exactly one minimal time-like surface of the third type with invariants
$(K, \varkappa)$.
