  We apply the symmetry reduction method of Roberts to numerically analyze the
linear stability of a one-parameter family of symmetric periodic orbits with
regularizable simultaneous binary collisions in the planar pairwise symmetric
four-body problem with a mass $m\in(0,1]$ as the parameter. This reduces the
linear stability analysis to the computation of two eigenvalues of a $3\times
3$ matrix for each $m\in(0,1]$ obtained from numerical integration of the
linearized regularized equations along only the first one-eighth of each
regularized periodic orbit. The results are that the family of symmetric
periodic orbits with regularizable simultaneous binary collisions changes its
linear stability type several times as $m$ varies over $(0,1]$, with linear
instability for $m$ close or equal to 0.01, and linear stability for $m$ close
or equal to 1.
