How does a router process a frame

Take a scenario where a router receives an ethernet frame which is encapsulating an IP Packet. The following are the operations that would be performed by the router. The router looks into the destination mac-address inside the frame and checks if it is intended for itself. If the mac-address is incorrect, the frame is dropped. If correct, the router would calculate and verify the FCS value of the frame. Once verified, the router would look into the destination IP address in the IP Packet. The router would then analyze it’s routing table and then see if a matching destination network is available in the table corresponding to the destination IP address. if no match is available, the packet is dropped. If a match is available, then the router would create a new frame for the exit interface and the IP Packet would be encapsulated in the new frame. The old frame would be discarded by the router.