The Signature represents visual object shape 2D contour in 1D to recognition shape of the objectQuery. This 1D shape representation translated into Centroid Distance Histogram (CDH) Gokaramaiah et al. (Comput Graph Image Process 25:357–370, 1974 [16]) to achieve invariant transformations such as translation, scale, rotation, flip. The CDH representation performs well in content-based image retrieval system with low computational complexity and this representation method insensitive to noise of boundary. The CDH fails to represent concave shape object because the signature function maps some of the angle to more than one length from the centroid to contour. This problem solved by modifying the shape signature function which returns the average centroid length when the angle difference between two contour points approximately equals to 0.873 by traversing contour points in a clockwise direction. The starting point for clock traversing is minimum distance point from the centroid to contour. The Average Centroid Lengths (ACL) converted into histogram which makes shape representation independent of transformations. To improve recognition, more information of contour obtained by first-order and second-order difference histogram of the modified signature. This first-order and second-order difference Gokaramaiah et al. (IEEE Comput Soc, 2010 [1]) shape signature represented as hierarchical ACL. This ACL representation suitable for the Handwritten symbol recognition because small changes in the contour of shape adopted in Hierarchical ACL representation. The Handwritten symbol recognized based on k-nearest neighbor classifier (k-NNC) on sample database symbols.