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Let R be a ring. A right R-module M is called GI-flat ifTorR1 (M,G) = 0 for every Gorenstein injective left R-module G. It isshown that GI-flat modules lie strictly between flat modules and copureflat modules. Suppose R is an n-FC ring, we prove that a finitely pre-sented right R-module M is GI-flat if and only if M is a cokernel of aGorenstein flat preenvelope K→F of a right R-module K with F flat. Then we study GI-flat dimensions of modules and rings. Various resultsin [6] are developed, some new characterizations of von Neumann regularrings are given.