Summary: The synchronic distance is a fundamental concept in a Petri net. Marked graphs form a subclass of Petri nets. Given a matrix D, we are interested in the problem of finding a marked graph whose synchronic distance matrix is D. It is wellknown that the synchronic disrance matrix of a marked graph is a distance matrix. In this letter, we give a matrix D such that D is a distance matrix and there does not exist a marked graph whose synchronic distance matrix is D.