Complex sentence: Since the National Association is not considered a Major League, this no-hitter is not recognized officially as the first no-hitter pitched, but it is, however, considered the first no-hitter pitched in a professional game.
Split into simpler sentences: Since the National Association is not considered a Major League, this no-hitter is not recognized officially as the first no-hitter pitched. It is, however, considered the first no-hitter pitched in a professional game.