This paper proposes a supervised hashing method for image retrieval that simultaneously learns a good image representation and a set of hash functions. The method consists of two stages. In the first stage, a pairwise similarity matrix S over training images is decomposed into a product of HH^T, where H is a matrix with each row being the approximate hash code for a training image. In the second stage, a deep convolutional network is used to learn the image representation and hash functions. The network is trained using the learned hash codes and optionally the discrete class labels of the images. The method is evaluated on three benchmark datasets with different types of images, showing superior performance gains over several state-of-the-art supervised and unsupervised hashing methods. The proposed method also has a faster coordinate descent algorithm in the first stage compared to existing methods. The results show that the proposed method achieves better search accuracy, especially when incorporating both approximate hash codes and image tags in training. The method is efficient and scalable, making it suitable for large-scale image retrieval tasks.This paper proposes a supervised hashing method for image retrieval that simultaneously learns a good image representation and a set of hash functions. The method consists of two stages. In the first stage, a pairwise similarity matrix S over training images is decomposed into a product of HH^T, where H is a matrix with each row being the approximate hash code for a training image. In the second stage, a deep convolutional network is used to learn the image representation and hash functions. The network is trained using the learned hash codes and optionally the discrete class labels of the images. The method is evaluated on three benchmark datasets with different types of images, showing superior performance gains over several state-of-the-art supervised and unsupervised hashing methods. The proposed method also has a faster coordinate descent algorithm in the first stage compared to existing methods. The results show that the proposed method achieves better search accuracy, especially when incorporating both approximate hash codes and image tags in training. The method is efficient and scalable, making it suitable for large-scale image retrieval tasks.