  A new, so called odd Gel'fand-Zetlin basis is introduced for the irreducible
covariant tensor representations of the Lie superalgebra gl(n|n). The related
Gel'fand-Zetlin patterns are based upon the decomposition according to a
particular chain of subalgebras of gl(n|n). This chain contains only genuine
Lie superalgebras of type gl(k|l) with k and l nonzero (apart from the final
element of the chain which is gl(1|0)=gl(1)). Explicit expressions for a set of
generators of the algebra on this Gel'fand-Zetlin basis are determined. The
results are extended to an explicit construction of a class of irreducible
highest weight modules of the general linear Lie superalgebra
gl(\infty|\infty).
