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Skew of an image fiber, which has more than ten thousands of cores in a common cladding, was measured by a novel measurement method for the first time. This method can measure the time-of-flight difference between individual cores over the whole area of an image circle. The measurement result reveals that a test 100-m-long image fiber has skew of 5 ps/m, and the time-of-flight distributes randomly in the whole area of the image circle due to nonuniformity of the core dimension. It is also experimentally shown that the skew of an image fiber increases by bending. The theoretical analysis reveals that the bending-induced skew depends neither on the radius of curvature nor the shape of the curve but it depends only on the number of turns it is wound. The numerical calculation of skew by using typical parameters of image fibers shows that the winding have to be restricted to less than five turns to achieve a transmission speed of over 1 Gb/s/ch. Finally, we propose a twisted image fiber and an "8-shaped" bobbin to suppress the skew due to bending.