Abstract: The orthogonal-motion based camera calibration is an important approach in active-vision based calibration. In general, each pair of orthogonal movings of a camera can generate a linear constraint on the camera's five intrinsic parameters, and five such motion pairs are sufficient to linearly calibrate the camera. However an open question is that under what conditions of such five pairs of orthogonal movings the resulting constraints can be independent. A common view is that if no three motions out of the five motion pairs are coplanar, the corresponding five constraints can be independent. In the paper, this problem is further investigated. In particular, we show that if three sets out of the five orthogonal motion sets happen to form a three-orthogonal motion set (i.e., three motions are mutually orthogonal), then even if no three motions among the total seven ones are coplanar, the resulting five constraints are not necessarily independent, and a concrete non-independent example is also provided.