Yes. The Prophet Muhammed s.a.s. was sinless.
Holy KORAN 33:33:
"Ve karne fî buyûtikunne ve lâ teberrecne teberrucel câhiliyyetil ûlâ ve ekımnes salâte ve âtînez zekâte ve atı’nallâhe ve resûlehu, innemâ yurîdullâhu li yuzhibe ankumur ricse ehlel beyti ve yutahhirakum tathîrâ(tathîran)." (Arabic verse in Latin letters)
Meaning: The Ahl-ul Bayt (household of the Prophet) is pure.
Word by word: "O people of the House! Allah only wishes to keep away the sin from you and to cleanse you with a thorough cleansing."
What Allah wishes, is already done. For he has created everything perfect.