The importance of a long-term relationship between a manufacturing firm and its supplier(s) has been emphasized in the literature on supply chain management. Essential to such a relationship is the coordination among participants in a supply chain. In order to sustain the relationship, the coordination should enhance the profitability of not only the manufacturer, but also the supplier(s). In this paper, we consider a particular supply chain situation in which the manufacturer coordinates, e.g., supports, its supplier's innovation that can eventually lead to supply cost reduction. Developing a mathematical model, we show that although the coordination could improve the manufacturing firm's own profitability, it might not be attractive to the supplier unless the supply cost reduction should ultimately increase the market demand to a certain extent. Under particular circumstances, if the market demand stays constant, the manufacturer's profit increase due to the coordination equals the amount of profit loss to the supplier. The analysis presents exact mathematical criteria to determine whether the coordination strategy can be agreeable to both the manufacturer and the supplier. Numerical examples are employed to show the applicability of the criteria. (C) 2000 Elsevier Science B.V. All rights reserved.