This paper presents an iterative training of neural networks for intra prediction in a block-based image and video codec. First, the neural networks are trained on blocks arising from the codec partitioning of images, each paired with its context. Then, iteratively, blocks are collected from the partitioning of images via the codec including the neural networks trained at the previous iteration, each paired with its context, and the neural networks are retrained on the new pairs. Thanks to this training, the neural networks can learn intra prediction functions that both stand out from those already in the initial codec and boost the codec in terms of rate-distortion. Moreover, the iterative process allows the design of training data cleansings essential for the neural network training. When the iteratively trained neural networks are put into H.265 (HM-16.15), -4.2% of mean BD-rate reduction is obtained, i.e. -1.8% above the state-of-the-art. By moving them into H.266 (VTM-5.0), the mean BD-rate reduction reaches -1.9%.