  In combination with the Grenander--Szeg\"o theorem, we observe that a relaxed
positivity condition on multipliers, milder than the basic %fundamental
requirement of the Nevanlinna--Odeh multipliers that the sum of the absolute
values of their components is strictly less than $1$, makes the energy
technique applicable to the stability analysis of BDF methods for parabolic
equations with selfadjoint elliptic part. This is particularly useful for the
six-step BDF method for which no Nevanlinna--Odeh multiplier exists. We
introduce multipliers satisfying the positivity property for the six-step BDF
method and establish stability of the method for parabolic equations.
