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Path marginal cost (PMC) is the change in total travel cost for flow on the network that arises when time-dependent path flow changes by one unit.Because it is hard to obtain the marginal cost on all the links, the local PMC, considering marginal cost of partial links, is normally calculated to approximate the global PMC.When analyzing the marginal cost at a congested diverge intersection,a jump-point phenomenon may occur.It manifests as a likelihood that a vehicle may unsteadily lift up (down) in the cumulative flow curve of the downstream links.Previously, the jump-point caused delay was ignored when calculating the local PMC.This article proposes an analytical method to solve this delay which can contribute to obtaining a more accurate local PMC.Next to that, use a simple case to calculate the previously local PMC and the modified one.The test shows a large gap between them, which means that this delay should not be omitted in the local PMC calculation.