Abstract: A analytical synthesis method of four-bar linkage in the special configtnation, in which the coupler curve has a four-point contact with its tangent (Ball's point), is Presented.With this method, the point which is on the expecting straight-line, the direction and two frame points,can be given beforehand.And some synthesizing formulae are derived and some synthesizing examples are given. The results have proved that the formulae are correct.