The following is from the wiki: http://en.wikipedia.org/wiki/Proper_morphism
Projective morphisms are proper, but not all proper morphisms are projective. For example, it can be shown that the scheme obtained by contracting two disjoint projective lines in some *P*$^3$ to one is a proper, but non-projective variety.
How to check it is non-projective? And I think it should be a morphism, how does it become a variety?