  We show that two parties far apart can use shared entangled states and
classical communication to align their coordinate systems with a very high
fidelity. Moreover compared with previous methods proposed for such a task,
i.e. sending parallel or anti-parallel pairs or groups of spin states, our
method has the extra advantages of using single qubit measurements and also
being secure, so that third parties do not extract any information about the
aligned coordinate system established between the two parties. The latter
property is important in many other quantum information protocols in which
measurements inevitably play a significant role.
