  The contribution of the tensor meson $K_2^*(1430)$ exchange in the process
$\gamma p\to K^+\Lambda(\Sigma^0)$ is investigated within the Regge framework.
Inclusion of the $K_2^*$ exchange in the $K(494)+K^*(892)$ exchanges with the
coupling constants chosen from the SU(3) symmetry leads to a better description
of the production mechanism without referring to any fitting procedure. This
shows the significance of the role of the tensor meson exchange to have the
Regge theory basically free of parameters with the SU(3) symmetry a good
approximation for the meson-baryon couplings.
