The Jordan canonical form basis states for an invertible chaotic map, the Baker map, are constructed. A straightforwardly obtained recursion formula is presented for construction of the Jordan states and of the spectral decomposition of the Frobenius-Perron evolution operator. Comparison of this method with earlier, subdynamics techniques demonstrates that it is much more direct and simpler. The physical significance of the Jordan states is approached from the point of view of an entropy evolution equation. The method is also applied to the Bernoulli map, yielding its eigenstates more straightforwardly than done previously. (c) 1997 American Institute of Physics.