A grave, in which horse bones (skull and distal parts of extremities) were found in addition to an equestrian skeleton, i. e. the grave with partially buried horse, was excavated at the cemetery from the Period of the Avar Khaganate in Cierny Brod. The most up to date catalogue of sites with occurrence of the partially buried animals on the Avar Khaganate territory is presented. Since more necropolises have not been completely published, the studied phenomenon is evaluated by quantitative method, only considering the number of sites but not the amount of the graves within them. This can cause some destortion, however, it does not influence the general picture of the occurrence of the graves with partially buried animals from the Period of the Avar Khaganate. The above-mentioned phenomenon is analysed in relation to the graves chronology and buried animal species. Although vast majority of these graves can be dated to the early phase of the Period of the Avar Khaganate, their occurrence in later periods (middle and late phases) does not seem to be rare either. In term of the animal species is concerned, horse is predominating, which is solely to be found in the male graves. On the contrary, the partial burials of cattle or sheep/goat are present also in the graves of women and subadult individuals. Occurrence of the studied phenomenon is supplemented with cartographic evaluation according to the animal species. Following maps of the sites, the highest concentration is found on the territory east of the Tisza River, mainly around town Szeged. The equestrian graves with the partially buried horses dated mostly to the early phase of the Period of the Avar Khaganate were excavated here. Graves with the partially buried animals, mostly those with horses, have numerous parallels in nomadic communities living in the East European steppe zone. Finally, the interpretation of this phenomenon is given. It is connected with Bulgarian Kutrigurs, whose military potential was integrated into the Khaganate's armed forces after the Avars had defeated them. The Kutrigurs probably settled the area of the Carpathian Basin - to the east of the Tisa River where the majority of such graves was found.