DNA profiling is currently the most widely used method for parentage verification, although many forms of it have limitations of some sort. In this paper, a general formula is derived to depict a simple relationship between the probability that a random man and the probably that a male relative of the child, other than the child's father, is excluded from paternity, when the phenotype of the child's mother is unavailable. With this, the possible limitations of a finite set of STR loci in excluding close relatives of the child from paternity are illustrated. Genetically, among the commonly encountered biologic relationships, to exclude a full sibling of the child from paternity if they pose themselves as father and child remains the most difficult.