Magnetic heat treatment has been carried out on a giant magnetostrictive alloy Tb0.36Dy0.64(Fe0.85Co0.15)2 with ⟨110⟩ crystal orientation. A dramatic improvement in magnetostriction along and perpendicular to the crystal axis (defined as λ‖ and λ⊥, respectively) occurs when cooling the sample through the Curie temperature TC under 240kA∕m applied perpendicular to its axis. When the applied annealing field was parallel to the crystal axis, the magnetostrictive behavior becomes “anomalous;” negative λ‖ and positive λ⊥ are obtained in low fields, accompanied with relatively low values in high fields. A single-{111}-twin model has been suggested to explain such differential magnetostrictive response.