Secret image sharing is a means of hiding an image within another image to generate similar images. In 1979, Shamir proposed a method of secret image sharing known as the (t, n) threshold scheme. (t, n) threshold schemes can generate n shadow images and any t of n shadow images can be used to reconstruct the secret image and cover image. Secret image sharing has two main parts: secret image sharing and secret image recovery. The goal of sharing is to embed a secret image in a cover image and reduce the distortion of the shadow image. The most important aspect of recovery is reconstructing the secret image with lossless. Many current schemes perform well at the first task, but most fail to recover the secret image successfully. To address this problem, we propose a novel method for secret image sharing based on a power-of-two Galois field rather than primes. Our experimental results showed that our scheme delivered satisfactory quality shadow images, while it could reconstruct secret images and cover images successfully with lossless.