This paper presents a supervised hashing method for image retrieval, which aims to automatically learn a good image representation and a set of hash functions. The method is divided into two stages: the first stage involves decomposing the pairwise similarity matrix into a product of hash codes using a scalable coordinate descent method, and the second stage learns the feature representation and hash functions using a deep convolutional network. The proposed method is evaluated on three benchmark datasets (MNIST, CIFAR-10, and NUS-WIDE) and shows superior performance compared to several state-of-the-art supervised and unsupervised hashing methods. The experimental results demonstrate that the proposed method achieves higher Mean Average Precision (MAP) and better precision curves, indicating its effectiveness in enhancing the hashing quality for images. Additionally, the proposed coordinate descent algorithm is shown to be more efficient than existing methods in terms of convergence speed and scalability.This paper presents a supervised hashing method for image retrieval, which aims to automatically learn a good image representation and a set of hash functions. The method is divided into two stages: the first stage involves decomposing the pairwise similarity matrix into a product of hash codes using a scalable coordinate descent method, and the second stage learns the feature representation and hash functions using a deep convolutional network. The proposed method is evaluated on three benchmark datasets (MNIST, CIFAR-10, and NUS-WIDE) and shows superior performance compared to several state-of-the-art supervised and unsupervised hashing methods. The experimental results demonstrate that the proposed method achieves higher Mean Average Precision (MAP) and better precision curves, indicating its effectiveness in enhancing the hashing quality for images. Additionally, the proposed coordinate descent algorithm is shown to be more efficient than existing methods in terms of convergence speed and scalability.