Let $\displaystyle V$ be a vector space, and let $\displaystyle W \subset V$ be its subspace. Is it true, that there exists a space $\displaystyle W'$ such that $\displaystyle V = W \oplus W'$?

It is clear for finite-dimensional spaces (you can work with bases, and matrices)! However i have no clue how to do this in the general case? Is it really true, or is there any counterexapmle?