Abstract: The multiplication of Dirichlet generating functions corresponds to the usual convolution of arithmetic functions. Although the convolution of multiplicative functions is multiplicative, the convolution of completely multiplicative functions need not be completely multiplicative. We show how a Hopf algebra structure on the positive integers suggests a modification of the convolution, such that the modified convolution of completely multiplicative functions is completely multiplicative. There is a corresponding notion of modified Dirichlet generating functions.