The System Dependence Graph (SDG) is a program representation that is the basis of program slicing, a technique that extracts the part of the program that can affect the values computed at a given program point (known as the slicing criterion). Several approaches have enhanced the SDG representation to deal with object-oriented programs, being the most advanced approach the Java System Dependence Graph (JSysDG). In this paper, we show that even the JSysDG does not produce complete slices in all cases when some object variables are selected as the slicing criterion. Then, we extend the JSysDG with the addition of a specific flow dependence for object type variables called object- flow dependence. This extension provides a more accurate flow representation between object variables and its data members and allows us to obtain complete slices when an object variable is considered as slicing criterion.