The retrial queuing system with general renovation is under investigation. The mechanism of general renovation with retrials means that the packet at the end of its service in accordance with a given probability distribution discards a certain number of other packets from the buffer and itself stays in the system for another round of service, or simply leaves the system without any effect on it. In order to obtain some probability and time related performance characteristics the embedded Markov chain technique is applied. Under the assumption of the existence of a stationary regime, the steady-state probability distribution (for the embedded Markov chain) of the number of packets in the system is obtained, as well as some other characteristics, such as the probability of the accepted task to be served or the probability of the accepted task to be dropped from the buffer, the probability distribution of number of repeated services. Also time characteristics are given.