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The scope of this paper is to look at some aspects of the differential geometry of Bezier curves in Minkowski space. For that purpose, we firstly introduce Frenet Bezier curve in Minkowski 3-space. Especially, we investigate the Serret-Frenet frame, curvature and torsion of the Frenet Bezier curves at all points. Moreover, we give the Frenet apparatus of these curves at the end points.