Exploiting modification direction (EMD) based data hiding techniques (DHTs) provide moderate data hiding capacity and high-quality stego images. The overflow problem and the cyclic nature of the extraction function essentially hinder their application in several fields in which reversibility is necessary. Thus far, the few EMD reversible DHTs are complex and numerically demanding. This paper presents a novel EMD-based reversible DHT using dual-image. Two novel 2 × 4 modification lookup tables are introduced, replacing the $256\times 256$ reference matrix used in similar techniques and eliminating the numerically demanding search step in similar techniques. In the embedding step, one of the modification tables modifies a pixel in odd columns in the first cover image and keeps its image in the second cover image intact. The other modification table modifies a pixel in even columns in the second cover image and keeps its image in the first cover image intact. This embedding strategy enables direct reversibility at almost zero computational cost. This technique embeds one $4-ary$ secret digit into each pixel in the first cover image and its image in the second cover image resulting in one bit per pixel (bpp) data embedding rate. The use of the $4-ary$ numbering system enables direct and numerically efficient conversion of the binary secret message to the $4-ary$ and vice versa. The advantages of the proposed algorithm are straightforward reversibility, simplicity, numerical efficiency, direct conversion of the binary secret message to $4-ary$ and vice versa, and elimination of the need for the $256\times 256$ reference matrix by replacing it with two 2 × 4 lookup tables. Simulation results show that the embedding rate of the proposed technique is one bpp. It achieved more than 49 dB average Peak to Signal Noise Ratio (PSNR) over all test images.