The concept of Morgan tree [6] is shown to be useful in generation of all non-isomorphic trees. Namely, to each tree one can assign canonical Morgan tree. Since, the number of Morgan trees [5, 1] is much larger then number of canonical Morgan trees, it is of interest to create an efficient algorithm that creates only a fraction of Morgan trees not eliminating the single canonical Morgan tree. Then, in the second step, non-canonical trees are eliminated. The rules for the recognition of non-canonical trees are proposed in [4, 3]. However, it seems that Rule 3 in [4] and Rule 1se in paper [3] are not correct. In this paper, we present the counter-examples to these rules.