An order-free second-order transitive-closure specification over a vocabulary $L$ is a specification whose three sentences are over $L$ and the copies of the block alone, with no order symbol. It defines, on any $L$-structure, the same graph on the assignments of the block and the same acceptance condition. A decision problem $P$ over $L$ is order-free SO(TC) definable when some such specification accepts, for every nonempty finite $L$-structure $A$, exactly when $A$ is a yes-instance of $P$: no linear order appears in the statement.