On this page one can find several editions of Palestrina's Jesu Rex admirabilis. I noticed that in a lot of them (such as this one), it starts with a half-note upbeat.
In others (such as this one), the score is shifted by a half-note, so it starts with an upbeat. Note that this induces syncopated harmony. (If you have the same harmony on a weak beat and on the following strong beat, it is called syncopated harmony, as in 'D' on this example). This is sometimes considered an error in music theory. Is this a wrong edition?