We investigated the group of 59 comets having various orbits and crossing Pluto's movement plane at a distance from 29.5 to 49.5 A.U. It is shown that the comets have relatively great perihelion distances and specific distribution of inclinations of orbits. Some irregularities are found in the distribution of longitudes of perihelions and remote nodes which are not typical of the total amounts of comets. Most of the nodes and perihelions of cometary orbits under investigation are concentrated in two opposite ranges of longitudes. The latitude of their perihelions is in good correlation with perihelion distance. A noticeable correlation between the parameters involved in Tisseran's criterion is seen. For «younger» comets with elliptical orbits, the distance of remote nodes correlates with their own distance of Pluto at appropriate longitudes. We made a conclusion on the existence of the Pluto's comet family.