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

Canonical Coordinates and Natural Equations for Minimal Time-like Surfaces in $R^4_2$