An overview of state of art in computerized object recognition techniques regarding digital images is revised. Advantages of shape based techniques are discussed. Importance of "Fourier Descriptor" (FD) for the shape based object representation is described. A survey for the available shape signature assignment methods with Fourier descriptors is presented. Details for the design of shape signature containing the crucial information of corners of the object are depicted. A novel shape signature is designed basing on the Farthest Point Angle (FPA) which corresponds to the contour point. FPA signature considers the computation of the angle between the line drawn from each contour point and the line drawn from the farthest corner point. Histogram for each 15o angle conceiving the information of the object is constructed. FPA signature is evaluated for three standard databases; viz., two in Kimia {K-99, K-216} and one in MPEG CE-1 Set B. The performance of the present FPA method estimated through recognition rate, time and degree of matching and is found to be higher.