Abstract: A novel search technique was presented for designing noncoherent unitary space-time constellation. First of all, a unitary matrix framework based on Grassmann manifold was defined. Under the constraint of this framework, a distance threshold was set by using the existing minimum chordal Frobenius norm of optimal packing distribution on the Grassmann manifold, and the points were searched for whose minimum chordal Frobenius norm exceeds the threshold by changing the amplitude and phase of every entry in the unitary matrix. At last, the whole unitary space-time constellation with minimum chordal Frobenius norm maximum was gotten. Numerical simulations indicate that this new constellation perfor better than the present codes.