An exact Sagdeev equation for arbitrary-amplitude solitary kinetic Alfvén waves in a non-thermal plasma is derived. For small β′, the proportion of fast electrons, an analytical expression for the exact pseudopotential V (φ) is obtained. For several values of β′, the Sagdeev potential V (φ) has been calculated by integrating the Sagdeev equation. It is found that, depending on the values of β′, both hump and dip solitons exist.