If we modify a binary tree with every leaf distinct, by making every link from parent to child into an undirected graph edge we have an acyclic undirected graph. What was the tree root has two edges and the leaves each have one. All the other nodes have three links. We add a honorary leaf at the root and we then have just two sorts of nodes. At that point we cannot see which node was the root and any node adjacent to a leaf can assume that role. We can thus turn that graph back into a binary tree choosing an arbitrary leaf, and discarding the chosen leaf. The new tree will have the same fringe except for a cyclic permutation. In this tree to tree transformation some of the nodes will have changed their parent. A node of a tree knows which child is its left, and which its right. When the parent changes we permute the roles cyclically (P, LC, RC). Any finite binary tree can be drawn on the 2D plane including the left-right distinction. This tree to tree transformation with the cyclic role permutation makes the same drawing suitable for both the old and new tree except for the deletion and addition of one leaf.