As described in the classic works of Lee--Stewart and Short--Stewart, the
numerical evaluation of linear stability of planar detonation waves is a
computationally intensive problem of considerable interest in applications.
Reexamining this problem from a modern numerical Evans function point of view,
we derive a new algorithm for their stability analysis, related to a much older
method of Erpenbeck, that, while equally simple and easy to implement as the
standard method introduced by Lee--Stewart, appears to be potentially faster
and more stable.