It is shown that an n-state two-way nondeterministic finite automaton (2NFA) over an alphabet Σ can be transformed to a one-way automaton (1NFA) with |Σ|·n12+1 states, where n12∼34πn3n is a trinomial coefficient. A close lower bound of n12 states is given for a four-symbol alphabet. To compare, for unrestricted alphabets, this transformation is known to require 2nn+1∼1πn4n states (Kapoutsis, “Removing bidirectionality from nondeterministic finite automata”, MFCS 2005).