This paper investigates the intonation system of Paraguayan Guarani in the Autosegmental-metrical (AM) framework of intonational phonology. Previous work on Guarani intonation stated that Guarani has two types of pitch accent, rising (L*+H or LH) and falling (H+L* or HL), and there is no prosodic unit between a word and an Intonational Phrase. But these findings seem to have resulted from the limitation of the data examined. When longer words/sentences and various syntactic structures are examined, it was found that Guarani has one type of pitch accent, a tritonal HLH*, and has an Accentual Phrase (AP). The tonal pattern of AP is /H HLH* Ha/, i.e., it has one pitch accent and its edges are marked by a H tone. However, because the pitch accent is tritonal, AP edge tones are realized only when there are unstressed syllables before and after the syllables carrying the tritonal pitch accent, suggesting that the function of AP boundary tone is not marking word prominence as in other AP languages. Instead, an important function of Guarani AP seems to mark specific syntactic categories and groupings. These findings are compared with other AP languages and discussed in terms of the typology of word-prominence type.