In view of recent experimental work, the neutron noise in a boiling water reactor is believed to be separable into local and global components. It is the existence of the local component that makes possible the measurement of steam velocity by correlating the signals of axially placed in-core neutron detectors. In the present paper, we use a one-dimensional (axial) model of the core and solve the two-group diffusion equations satisfied by the neutron noise. The solution is shown to be composed of two terms that can be identified as the theoretical counterparts of the components found in experiments. The properties of the two terms are discussed in the special case of an axially propagating disturbance of the moderator density (steam content).