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In [1, 2], L. Carlitz constructed a $q$-Eulerian numbers, by using $q$-difference operator. In this paper, we give another constructions of a $q$-Euler numbers, which are different than his $q$-Euler numbers (see , ). By using our $q$-Euler numbers, we can investigate the relations between $q$-Euler numbers and $q$-extension of Genocchi numbers.