  We propose a notion of a super n-Lie algebra and construct a super n-Lie
algebra with the help of a given binary super Lie algebra which is equipped
with an analog of a supertrace. We apply this approach to the super Lie algebra
of a Clifford algebra with even number of generators and making use of a matrix
representation of this super Lie algebra given by a supermodule of spinors we
construct a series of super 3-Lie algebras labeled by positive even integers.
