This article proposes a new regional eigenstructure assignment via rank-one LMI approach. A gain parameter condition for the regional eigenvalue/eigenstructure assignment is newly derived. This assignment condition is easily combined with H design by means of enhanced LMI characterisation. In the present approach, the desired assignment of closed-loop eigenvalues (i.e. poles) are not previously fixed but constrained into individual assignment regions to bring us more design freedom than classical exact assignment. The regional assignment discussed in this article never falls into an ordinary LMI root clustering because the union of assignment regions is disjoint in general. Each closed-loop eigenvector is also constrained into individual alignment cone. To show the practical use of the extra design freedom brought by regional assignment, a transient response shaping in H design is also discussed. A useful design algorithm based on linearisation algorithm is proposed.