Using transforms in video coding is an effective method in reducing the spatial redundancy. However, for some cases applying transforms does not reduce the spatial redundancy. For these cases, transforms are skipped and the prediction error is directly quantized and then entropy coded. To further reduce the spatial redundancy in the transform skipped blocks, a pixel-by-pixel lossy intra prediction method based on a two dimensional correlation model is proposed in this paper. In the proposed method, three reconstructed neighboring pixels are used to obtain the prediction. Neighboring pixels and the prediction weights change depending on the selected intra mode. The results of the experiments on different test classes in HEVC version 1 and HEVC Range Extension (RExt) reference softwares show that the proposed method can achieve gains up to approximately 0.5% BD-rate for All-Intra lossy coding compared to HEVC version 1 and the Range Extensions of the HEVC.