  The purpose of this paper is to construct the law of a L\'evy process
conditioned to avoid zero, under mild technicals conditions, two of them being
that the point zero is regular for itself and the L\'evy process is not a
compound Poisson process. Two constructions are proposed, the first lies on the
method of $h$-transformation, which requires a deep study of the associated
excessive function; while in the second it is obtained by conditioning the
underlying L\'evy process to avoid zero up to an independent exponential time
whose parameter tends to $0.$ The former approach generalizes some of the
results obtained by Yano \cite{Yano10} in the symmetric case and recovers some
of main results in Yano's work \cite{Yano13}, while the latter is reminiscent
of \cite{Chaumont-Doney05}. We give some properties of the resulting process
and we describe in some detail two examples: alpha stable and spectrally
negative L\'evy processes.
