According to Yahoo Answers:

To be “completely unbiased” simply means to see things without prejudice, external influences and having the ability to see things guided wholly on reason. To be completely unbiased is rather humanly impossible, however with a conscious effort we are able to at least strive to such a state.

Unbiased-ness doesn’t relate to self-contradiction persay, not unless you were confusing “biased” with personal opinion, which is indirectly related to biases in some instances, but not synonymous.

Unbiased-ness also doesn’t mean one can not stick to one’s own opinion, since one’s opinion can be guided by reason (which is independent from our basic personal sentiment) as opposed to an external influence such as prejudice, subjective experiences, etc.

The best thing to do is to check if you are indeed biased and wikipedia has a list of congnitive biases which you can look at here.