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It is well-known that a number of convolutional neural networks (CNNs) generate checkerboard artifacts in both of two processes: forward-propagation of upsampling layers and backpropagation of convolutional layers. A condition for avoiding the artifacts is proposed in this paper. So far, these artifacts have been studied mainly for linear multirate systems, but the conventional condition for avoiding them cannot be applied to CNNs due to the non-linearity of CNNs. We extend the avoidance condition for CNNs and apply the proposed structure to typical CNNs to confirm whether the novel structure is effective. Experimental results demonstrate that the proposed structure can perfectly avoid generating checkerboard artifacts while keeping the excellent properties that CNNs have.