Let f and g real functions of two variables and ∇2f(x,y)=[fxx,fxy,fyx,fyy]. We consider the polynomials orthogonal with respect to the inner product: ⟨f,g⟩S=c∫Ω∇2f(x,y)⋅∇2g(x,y)W(x,y)dydx+λf(c1,c2)g(c1,c2), where (c1,c2) is some corner point in Ω=[a1,b1]×[a2,b2], λ>0, and c=1/∫ΩW(x,y)dxdy. We study the particular cases when W(x,y) correspond to the product of the weight of Laguerre polynomials and Gegenbauer polynomials.