A linkage is a collection of line segments, called bars, possibly joined at their ends, called joints. We consider flattening a tree-like linkage, that is, a continuous motion of their bars from an initial configuration to a final configuration looking like a"straight line segment," preserving the length of each bar and not crossing any two bars. In this paper, we introduce a new class of linkages, called "radial trees," and show that there exists a radial tree which cannot be flattened.