What is a non-denominational church?

Some Christians claim a non-denominational church is better. However, as a scientist I like to see all angles of the story: I was under the impression that since all Christians don't belong to **one church**, (They agree to disagree on Ephesians 4 and opt for the Nicene Creed) then all Christians doctrines are denominations - there by:
1c penny doctrine,
5c nickel doctrine,
10c dime doctrine,
25c quarter doctrine,
50c half-dollar doctrine, etc
= 1.00 dollar Eph 4 Church - some claim all Christians are part of the universal church. I like the idea that non-denominational churches reject the idea of a denominational structure and opt for autonomous churches. This is similar to Paul when he opted not take money from the Corinthians but still claimed to have authority over them. Maybe that is what non-denominational is, that there is no central government and only Christ is the head or leader? So if non-denominational or denominational has nothing to do with doctrine. That begs the question: What is the definition of the One Doctrine in Eph 4? Or, simply explain: What is a non-denominational church?