there are 3 Bar-Buttons in the UINavigationItem:
But there is no "nextBarButtonItem" (= rightBarButtonItem with arrow). How can I create it? Do I need an own image with an arrow? How can I put the image in the rightBarButtonItem? Or is there a better way without image?

The only way is to use a bar button item with a custom image with that next-button look, and set it as rightBarButtonItem. Apple doesn't provide any nextBarButtonItem functionality due to the way a navigation controller works.
If you look carefully at the Now Playing button in the iPod app it's also custom-designed.
Check three20 library used to create Facebook app for iPhone.
https://github.com/facebook/three20
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