Let f be an odd, C2 function on [− 1, 1], which vanishes at ± 1, and such that f′(O) < 0, f′ (±1) > 0 and u ↦ f(u)/u is increasing. Dang, Fife and Peletier  showed that there is a unique solution u with values in [−1, 1] of
which has the same sign as xy. The linearised operator around u is B defined by
It is proved here that the spectrum of B contains at least one negative eigenvalue, that all eigenfunctions corresponding to negative eigenvalues have the symmetries of the square, and that for Allen–Cahn's nonlinearity (f(u) = 2u3 − 2u), there is exactly one negative eigenvalue.