This paper presents a quantitative model for designing a strategy map. A strategy map is a representation of the cause-effect relationships between strategic objectives of a Balanced Scorecard (BSC). The work is based on an early work of the authors, where the Analytic Hierarchy Process (AHP) is used to formulate a manufacturing strategy and to generate performance indicators for the manufacturing area. This work takes the hierarchical model representing the manufacturing strategy to represent a strategy map and then uses AHP techniques to obtain the priorities of the relationships (arcs) and to decide which relationships are important. One contribution of the paper is that the proposed method has the objective of estimating the priorities of the arcs, instead of priorities of the nodes of the hierarchy, opposite to what AHP does. As an illustration, the case of a fishing company is presented.