Researchers have developed a great number of embedding techniques in steganography. Matrix embedding, otherwise called the binning scheme, is one such technique that has been proven to be an efficient algorithm. Unlike conventional matrix embedding, which requires a maximum likelihood decoding algorithm to find the coset leader, this study proposes an adaptive algorithm called the linear independent approximation embedding (LIAE) algorithm. There are numerous concerns with the cover location selection, such as less significant cover to be modified, alterable part of the cover and forced the cover to be modified, when embedding a secret message into the cover. The LIAE algorithm has the ability to perform data embedding at an arbitrarily specified cover location. Therefore, the embedded message can be identified at the receiver without incurring any damage to the associated cover location. The simulation results show that the LIAE embedding algorithm has superior efficiency and adaptability compared with other suboptimal embedding algorithms. Moreover, the experimental results also demonstrate the trade-off between embedding efficiency and computational complexity. (14 refs)