We report on measurement of the muon Knight shift in single crystals of LiV(2)O(4). Contrary to what is anticipated for the heavy fermion state based on the Kondo mechanism, the presence of inhomogeneous local magnetic moments is demonstrated by the broad distribution of the Knight shift at temperatures well below the presumed 'Kondo temperature' ([Formula: see text] K). Moreover, a significant fraction ([Formula: see text]) of the specimen gives rise to a second component which is virtually non-magnetic. These observations strongly suggest that the anomalous properties of LiV(2)O(4) originate from frustration of local magnetic moments.