In the lossless compression schemes of the H.26X series video coding standards, the residuals obtained by intra-frame prediction still retain strong spatial correlation and directly participating in entropy coding will lead to the decrease in coding efficiency. Unlike natural images, intra-frame prediction residuals contain rich edge features. To utilize the special spatial correlation of residuals, further reducing its spatial redundancy and improving the intra-frame coding efficiency, a universal lossless intra-frame coding algorithm based on residual median edge detection was proposed. The algorithm first performed edge detection on the intra-frame prediction residuals step by step. By analyzing the numerical features of the adjacent residuals, the median edge detection algorithm was applied to obtain new prediction value. Then, new prediction residual was obtained by comparing prediction value and original residual value. Finally, according to whether the energy of the current coding unit was reduced, it could quickly determine whether to use the new residuals for entropy coding, so as to ensure that the coding of the new prediction residuals could improve the compression ratio. Experimental results show that the coding units processed by this algorithm had lower spatial redundancy and residual energy, thereby reducing the bit-rate after entropy coding. Applying the proposed algorithm in H.265 and the latest H.266 standards, the average energy of residuals decreased by 67.9%, and the average bit-rate reduced by 7.04% and 5.98% respectively, while the codec time changed slightly, with significant practical value.