AbstractThe problem of updating shortest paths from all the vertices to a set of vertices when the length function is decreased was considered by S. Goto and A. Sangiovanni‐Vincentelli and a solution algorithm was presented based on the LU‐factorization of the measure matrix and a matrix inversion formula. The present paper shows that the problem can be solved by means of the Dijkstra method in a running time of the same order as Goto and Sangiovanni‐Vincentelli's algorithm, assuming a smaller amount of initial data than theirs, i.e., we do not need the LU‐factorization of the measure matrix.