We propose an implicit interval Newton algorithm for finding a root of a nonlinear equation. Our implicit process avoids the burden of selecting an initial point very close to the root as required by the classical Newton method. The conventional interval Newton method converges quadratically, while our modified algorithm converges cubically under some conditions and bi-quadratically under other conditions. These convergence results are proved using an image extension of a Taylor expansion. The algorithm is illustrated by numerical examples, and we provide a comparison between the existing interval Newton method and our proposed method.