Abstract: Recently, Jerk equation which is the third-order explicit autonomous differential equation is noticed to be a motivating sub-class of dynamical systems. Where many of regular and chaotic motion features can be reveal from these systems. In this study, a simplified version Jerk map is presented. Different properties of dynamical behavior is acquired by replacing three dimensional systems to two dimensional one. Where a new parameter is added with the same properties. Moreover, we study the fixed point of modified Jerk map with the form Mja.b = (y-ax+by2) = (xy) and the general properties of them, so, we find the contracting and expanding area of this map. Also, we determine fixed point attracting repelling or saddle.