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In our previous work we have shown that the invariant varieties of periodicpoints (IVPP) of all periods of the 3 dimensional Lotka-Volterra map can bederived, iteratively, from the singularity confinement (SC). The methoddeveloped there can be applied to any integrable maps of dimension $d$ onlywhen the number of the invariants $p$ equals to $d-1$. We propose, in thisnote, a new algorithm of the derivation which can be used in the cases ${d\over2}\le p\le d-2$. Applying this algorithm to the 3 point Toda map, we derive aseries of its IVPP's.

Derivation of Invariant Varieties of Periodic Points from Singularity Confinement in the case of Toda Map