Reversible Data Hiding (RDH) is one of the most well-known methods adopted for concealed communication. One of the major issues in RDH is the overflow/underflow which exists in almost all the embedding techniques. This is a major issue which hinders the hiding capacity in many existing techniques. In the proposed novel LSB ODD/EVEN embedding algorithm, neither histogram modification (which involves shifting) nor difference expansion (which involves shifting and expansion of error) techniques are involved. No overflow/underflow problem is reported in the proposed method and involves multi-layer embedding. Performance of this approach or any data hiding schemes are usually measured in terms of MSE, PSNR, and SSIM. This approach is tested over standard test images that includes medical images also and compared with well-known existing schemes. © 2020, Ubiquitous International. All rights reserved.