An inkjet printer is operated to print an ink image and clear inkjets simultaneously. The inkjet printer delivers to a first inkjet in a printhead a first signal that ejects an ink drop from the first inkjet that corresponds to a pixel of an ink image stored in a memory of the printer and delivers to at least one other inkjet in the printhead a second signal that ejects an ink drop from the at least one other inkjet that does not correspond to a pixel of the ink image stored in the memory of the printer.