Diverse types of local GABAergic interneurons shape the cortical representation of sensory information. Here we show how somatostatin-expressing interneurons (SOM cells) contribute to odor coding in mouse olfactory cortex. We find that odor-tuned SOM cells regulate principal cells through a purely subtractive operation that is independent of odor identity or intensity. This operation enhances the salience of odor-evoked activity without changing cortical odor tuning. SOM cells inhibit both principal cells and fast-spiking interneurons, indicating that subtractive inhibition reflects the interplay of multiple classes of interneurons.