Unranked tree languages are valuable for modelling structured objects such as XML documents, database entries, and dependency trees. We introduce a new type of automaton for unranked tree languages, called Z-automaton. The model is closely related to stepwise tree automata, thus offering a compact form of representation, but it avoids obfuscating encoding schemes. We discuss alternative semantics and normal forms, and finally prove the membership problem to be in O(mn), where m is the size of the transition table, an n is the size of the input tree.