Reversible Steganography had been a crucial topic when perceptual quality and security is concerned. There is a trade-off between these two parameters since when high security is obtained the perceptual quality of the stego image is decreased. The block based self-secured LSB embedding scheme (BBSS-ES) proposed in this work is able to maintain both the metrics with very low computational cost. The scheme similar to pseudo random and chaotic LSB embedding scheme provides better security to secret message while maintaining better stego quality. It uses the center pixel to find the position in 3 × 3 neighbourhoods from where the LSB embedding would start. The index in the neighbourhood is simply calculated using natural logarithm over the magnitude of the center pixel. The embedding process continues in clockwise direction in the neighbourhood. The immunity of the proposed scheme to unwanted noise or attack in stego image is high at values of center pixel greater than equal to 12 since the offset in band after value 12 goes on increasing and any unwanted noise or attack would not be able to shift the value beyond the limit of the band. The system is evaluated over four cover and four secret images and the performance is measured in terms of peak signal to noise ratio with perceptual quality of the stego image.