Summary: Previous methods for exact linearization by feedback have relied on solving Frobenius systems of partial differential equations of dimensions equal to the Kronecker indices. We describe an algorithm whereby one may find the linearizing feedback for any controllable linearizable system having distinct Kronecker indices with \(p\)-controls by purely algebraic calculations and integration of at most \(p\) one-dimensional Frobenius systems. The paper concludes with a concrete example considered by L. R. Hunt, Renjeng Su and G. Meyer [Differential geometric control theory, Proc. Conf., Mich. Technol. Univ. 1982, Prog. Math. 27, 268-298 (1983; Zbl 0543.93026)].