This paper studies the subset of the non-Strebel points in the universal Teichmüller space T. Let z0 ∈△ be a fixed point. Then we prove that for every non-Strebel point h, there is a holomorphic curveγ . [0, 1] → T with h as its initial point satisfying the following conditions.(1) The curve γ is on a sphere centered at the base-point of T, i.e. dT(id, γ(t)) = dT(id, h), (t ∈ [0, 1]).(2) For every t ∈(0, 1], the variability set Vγ(t)[zo] of γ(t) has non-empty interior, i.e. Vγ(t) [z0] ≠φ.