At frequencies above the range at which low-frequency-generation noise is dominant, thermal noise in the channel is the main noise source of a junction field-effect transistor. Starting from the well known current and continuity equations, the drain- and gate-noise spectra and their correlation coefficient are calculated by means of a series expansion, in a second-order approximation. The results are compared with calculations and measurements of other authors. There is good agreement with experiments, but differences exist with some of the earlier computations in the literature.