Model checking has been successfully applied to system verification. However, there are no standard and universal tools to date being applied for system modification. This paper introduces a formal approach called the Linear Temporal Logic (LTL) model update for system modification. In contrast to previous error repairing methods, which were usually simple program debugging and specialized technical methods, our LTL model update modifies the existing LTL model of an abstracted system to correct automatically the errors occurring within this model. We introduce three single operations to represent, update, and simplify the updating problem. The minimal change rules are then defined based on such update operations. We show how our approach can eventually be applied in system modifications by illustrating an example of program corrections and characterizing some frequently used properties in the LTL Kripke model.