A funtion f is said to be lebesgue integrable on [a,b]c R if and only if there is a function F which is absolutely continuous on [a,b] such that its derivative F'(x)=f(x) almost everywhere on [a,b]. denjoy defined his special Denjoy intergral by a menthod of extension of the lebesgue integral, i.e.a function f is said to be special Denjoy integrable on [a,b] if there is a function F which is countinuous and ACG' on [a,b] such that its derivative F'(x)=f(x) almost everywhere on [a,b]. This study was intended to generalize the special Denjoy integral in the real line to the Euclidean space Rn. The generalization was done to the definitions and properties of the special Denjoy integral. This study was based on the interval function on I (E), the collection of a cell E c Rn. In doing such a generalization, we always maintained that the definitions and properties in the real line were kept as their special case.