Let G be a simple linear algebraic group defined over C and P ∪ G a maximal proper parabolic subgroup such that m:= dimCG/P ≥ 5. Let i:Z1∩ Z2 right arrow, hooked G/P be a smooth complete intersection such that degree Zi ≥ (m-1) ·index (G/P)/m, i=1, 2. Then the vector bundle i*T(G/P) → Z1 ∩ Z2 is semistable. © Taylor & Francis Group, LLC.