Anderson and Neven (1991) show that central agglomeration is a unique location equilibrium for n firms if firms play Cournot competition and discriminate over space in a linear city model. Matsushima and Shimizu (2005) reconfirm this result, under the condition, which the consumer density at the center of the line market is not small. This paper employs a framework a la Anderson and Neven (1991), but slightly modifying the market-serving condition and taking into consideration the stability conditions. It is shown that the location equilibrium for n firms can be of either spatial dispersion or central agglomeration, depending on the magnitude of transport rates. Furthermore, this paper also derives a general pattern of the location configuration for an odd and an even number of firms, respectively.