William Lee's invention in 1589 of the stocking frame was remarkable, because it was an invention of a complete new machine. At the time, it stood on its own as a production machine with many small parts made to a high level of accuracy. This paper outlines the growth of hand-knitting in the 16th century and shows how Lee's machine derived from peg knitting. Constructional details and the mode of operation are closely described. An account is given of the development and use of the frame-knitting machine in Britain and France. Finally, the invention is related to the state-of-the-art in other machinery of the time.