  Given an $n$-ary
  $k-$valued function $f$, $gap(f)$ denotes the essential arity gap of $f$
which is the minimal number of essential variables in $f$ which become fictive
when identifying any two distinct essential variables in $f$. In the present
paper we study the properties of the symmetric function with non-trivial arity
gap ($2\leq gap(f)$). We prove several results concerning decomposition of the
symmetric functions with non-trivial arity gap with its minors or subfunctions.
We show that all non-empty sets of essential variables in symmetric functions
with non-trivial arity gap are separable.
