Theorem 1. Given an ordinal $\Theta$ is a model $M$ of ZFC such that for every $\alpha < \Theta$, $M\vDash HOD^{\alpha+1} \ne HOD^\alpha$. The model $M$ in Theorem 1 is a generic extension f the constructible universe. The basic idea is to add generic branches to $\kappa$ Suslin trees in L. The r sult is obtained by the construction of trees in L that have suitable automorphism properties.