Abstract: The outline-drawing in squared paper design is to modify boundaries of given4-connected regions representing figures in a squared paper picture.Based on someconcepts about the set of boundary points in a digital picture,the paper gives amathematical description to the requirements of outline-drawing,and in analogyto the handed work,reguards the modification of boundaries as the expanding andshrinking of edges.In order to make sure of neccessary modifications automatically,the paper regards the boundaries of 4-connected regions satisfying a certain kind ofoutline-drawing as a boundary pattern,and thus put forward a syntax-directed exp-anding-shrinking method.The method is suitable for the realization of an interactiveprocessing in computer and therefore can be applied in CAD of squared paper design.