This paper introduces the Cartesian Atomic Cluster Expansion (CACE) method for machine learning interatomic potentials. CACE is a mathematically equivalent and simpler alternative to existing methods that use spherical harmonics and Clebsch-Gordan contraction to maintain rotational symmetry. Instead, CACE performs all operations in Cartesian coordinates, providing a complete set of polynomially independent features of atomic environments while maintaining interaction body orders. The method integrates low-dimensional embeddings of chemical elements, trainable radial channel coupling, and inter-atomic message passing. The resulting potential, CACE, exhibits good accuracy, stability, and generalizability. CACE is validated on diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys. It outperforms other MLIPs in terms of accuracy and stability, particularly in high-temperature simulations and extrapolation to unseen elements. The CACE framework is efficient, with a low memory consumption and the ability to scale well in MD simulations. It is implemented using PyTorch and is publicly available on GitHub. The method is also applicable to other MLIPs that use the ACE framework or E(3) equivariant message passing neural networks. CACE provides a complete and body-ordered description of atomic environments, which is essential for accurate and stable interatomic potentials. The method is also capable of alchemical learning, allowing for the extrapolation to unseen elements and configurations. The CACE potential is shown to be accurate and stable, with performance comparable to the most accurate potentials to date. The method is efficient, with a low computational cost and the ability to scale well in MD simulations. The CACE potential is a promising approach for machine learning interatomic potentials, offering a balance between accuracy, stability, and computational efficiency.This paper introduces the Cartesian Atomic Cluster Expansion (CACE) method for machine learning interatomic potentials. CACE is a mathematically equivalent and simpler alternative to existing methods that use spherical harmonics and Clebsch-Gordan contraction to maintain rotational symmetry. Instead, CACE performs all operations in Cartesian coordinates, providing a complete set of polynomially independent features of atomic environments while maintaining interaction body orders. The method integrates low-dimensional embeddings of chemical elements, trainable radial channel coupling, and inter-atomic message passing. The resulting potential, CACE, exhibits good accuracy, stability, and generalizability. CACE is validated on diverse systems, including bulk water, small molecules, and 25-element high-entropy alloys. It outperforms other MLIPs in terms of accuracy and stability, particularly in high-temperature simulations and extrapolation to unseen elements. The CACE framework is efficient, with a low memory consumption and the ability to scale well in MD simulations. It is implemented using PyTorch and is publicly available on GitHub. The method is also applicable to other MLIPs that use the ACE framework or E(3) equivariant message passing neural networks. CACE provides a complete and body-ordered description of atomic environments, which is essential for accurate and stable interatomic potentials. The method is also capable of alchemical learning, allowing for the extrapolation to unseen elements and configurations. The CACE potential is shown to be accurate and stable, with performance comparable to the most accurate potentials to date. The method is efficient, with a low computational cost and the ability to scale well in MD simulations. The CACE potential is a promising approach for machine learning interatomic potentials, offering a balance between accuracy, stability, and computational efficiency.