How somatosensory cortex (S1) encodes complex patterns of touch, as occur during tactile exploration, is poorly understood. In mouse whisker S1, temporally dense stimulation of local whisker pairs revealed that most neurons are not classical single-whisker feature detectors, but instead are strongly tuned to 2-whisker sequences involving the columnar whisker (CW) and one, specific surround whisker (SW), usually in SW-leading-CW order. Tuning was spatiotemporally precise and diverse across cells, generating a rate code for local motion vectors defined by SW-CW combinations. Spatially asymmetric, sublinear suppression for suboptimal combinations and near-linearity for preferred combinations sharpened combination tuning relative to linearly predicted tuning. This resembles computation of motion direction selectivity in vision. SW-tuned neurons, misplaced in the classical whisker map, had the strongest combination tuning. Thus, each S1 column contains a rate code for local motion sequences involving the CW, providing a basis for higher-order feature extraction.