The versified play Henry VIII is nowadays widely recognized to be a collaborative work not written solely by William Shakespeare. We employ combined analysis of vocabulary and versification together with machine learning techniques to determine which authors also took part in the writing of the play and what were their relative contributions. Unlike most previous studies, we go beyond the attribution of particular scenes and use the rolling attribution approach to determine the probabilities of authorship of pieces of texts, without respecting the scene boundaries. Our results highly support the canonical division of the play between William Shakespeare and John Fletcher proposed by James Spedding, but also bring new evidence supporting the modifications proposed later by Thomas Merriam.