1. A printing apparatus comprising: a printer engine configured to perform print processing based on a print job; at least one processor connected to at least one memory, the at least one processor and at least one memory configured to: acquire update firmware for updating firmware of the printing apparatus by downloading the update firmware; execute decompression processing of decompressing, after reception of the update firmware by downloading the update firmware is completed, the acquired update firmware; and update the firmware of the printing apparatus using the decompressed update firmware, wherein upon condition that a new print job causing the printer engine to print occurs after having started execution of the decompression processing and before finishing the decompression processing, the decompression processing is suspended from being executed, and wherein in a case where the decompression processing is completed, said printing apparatus is shifted to an update mode in which the print job cannot be executed, and the firmware of the printing apparatus is updated using the decompressed update firmware after the printing apparatus has been shifted to the update mode.