In this note we show that for finite-dimensional Bernstein algebras over a field of characteristic different from 2: 1.(1) The principal nilpotency of an element implies its strong nilpotency. 2.(2) If Ker (ω) is a nil algebra, then it is a train algebra. 3.(3) Every train algebra of dimension n⩽ 5 is special train algebra, and that is a best possible result.