The Pedigree from National Library of Ireland - Registered Pedigrees. All the pages have been merged to a single (large!) digital page.
The pedigree purports to show the descent from Howell Dha, King of Wales A.D, 948, through William de Barri (m. Angharad), The Mac Adam Barrys of Rathcormac, the Barrys and Green Barrys of Ballyclogh and the the Barrys of Killshanny and Ballinahiney/ Ballinahina.
Note that it is generally accepted that Angharad who married william de Barri was daughter of Nesta by her 2nd (?) partner - Gerald of Windsor not her 3rd (?) partner Stephen.
Click on the link below to see the pedigree, but be aware that it is necessarily, a very large file (12 mb)