The higher-order growth rate of instability for obliquely propagating kinetic Alfvén and ion-acoustic solitons in a magnetized non-thermal plasma have been obtained by the multiple-scale perturbation expansion method developed by Allen and Rowlands (1993). The growth rate of instability is obtained correct to order k2, where k is the wave number of a long-wavelength plane-wave perturbation. The corresponding lowest-order stability analysis has been considered recently by Bandyopadhyay and Das (2000b). It has been found that the kinetic Alfvén solitary waves are stable at the order of k but are unstable at the order of k2. It has also been found that the growth rate of instability at the order of k for ion-acoustic solitary waves is free from the parameters of the non-thermal plasma but at the order of k2 depends on the parameters of the non-thermal plasma.