Śliwa, Wiesław2011-03-072011-03-072001-06Indag. Mathem., (N.S.), 12(2),261-271.http://hdl.handle.net/10593/926Let E be an infinite-dimensional non-archimedean Frechet space which is not isomorphic to any of the following spaces: $c_0,c_0 x K^N,K^N$. It is proved that E contains a closed subspace without a Schauder basis (even without a strongly finite-dimensional Schauder decomposition). Conversely, it is shown that any closed subspace of $c_0 x K^N$ has a Schauder basis.enArticle