This paper presents a new sample-level filtering order for the Deblocking Filter process of the H.264/AVC video coding standard to be used instead of the traditional block-level order presented in previous works. This processing order allows a better exploration of the parallelism in the filtering process by reducing data dependencies in comparison to other works. The proposed sample-level order allows four parallel and independent samples filtering simultaneously, completing one complete macroblock filtering in fewer cycles and requiring less memory space than the related works. The proposed filtering order can be applied to the Deblocking Filter presented in a conventional H.264/AVC encoder or decoder and to the H.264/SVC interlayer Deblocking Filter. When compared to the original H.264/AVC filter and to the best related work found in the literature, the proposed scheme achieves a reduction of 72% and 25% in the number of clock cycles and a memory usage decrease of 75% and 43%, respectively.