This paper proposes a spatio-temporal feature using three-way cross-correlations of local motion attributes for action recognition. Recently, the cubic higher-order local auto-correlations (CHLAC) feature has been shown high classification performances for action recognition. In previous researches, CHLAC feature was applied to binary motion image sequences that indicates moving or static points. However, each binary motion image lost informations about the type of motion such as timing of change or motion direction. Therefore, we can improve the classification accuracy further by extending CHLAC to multivalued motion image sequences that considered several types of local motion attributes. The proposed method is also viewed as an extension of popular bag-of-features approach. Experimental results using two datasets shows proposed method outperformed CHLAC features and bag-of-features approach.