My iPhone Keeps Songs Even After I Delete Them?

I've followed all the directions for deleting songs off my iPhone. I uncheck the little boxes next to the songs I do not want and then sync my iPhone. However, I noticed after the first time I did this, the songs I had removed from my phone were still present. They were not able to be played, but the title still appears in my playlist. I'd like to fully remove them.

You have to delete the actual file, iTunes normally serves a link to the song.

To fully delete song off your iPhone do the following:
1. Search for the actual song file ( if you have a windows PC; Start menu, search the name of the song, and delete the file)
2. Open iTunes and find the song, it should have a symbol on the left side that looks like this:!
3. Double click the song, it should give you a message that the file is missing. Thus the song has been removed
4. Finally delete the song on iTunes and you are done.