Centerline extraction of the carotid artery in MRI is important to analyze the artery geometry and to provide input for further processing such as registration and segmentation. The centerline of the artery bifurcation is often extracted by means of two independent minimum cost paths ranging from the common to the internal and the external carotid artery. Often the cost is not well defined at the artery bifurcation, leading to centerline errors. To solve this problem, we developed a method to cooperatively extract both centerlines, where in the cost to extract each centerline, we integrate a constraint region derived from the estimated position of the neighbor centerline. This method avoids that both centerlines follow the same cheapest path after the bifurcation, which is a common error when the paths are extracted independently. We show that this method results in less error compared to extracting them independently: 10 failed centerlines Vs. 3 failures in a data set of 161 arteries with manual annotations. Additionally, we show that the new method improves the non-cooperative approach in 28 cases (p < 0.0001) in a data set of 3,904 arteries.