Muhammad al-Maghrabi, 41, was killed as he lay on the floor following his conviction over the death of the little girl, Rana Yahya Al-Matari.
His execution, at point blank range, was broadcast on live TV across Yemen.
He was shot dead in front of a crowd of thousands of people, including many who recorded what happened on their mobile phones, in the capital city of Sanaa.
His hands were tied behind his back as he was led from a prison van before being laid down on a rug in front of the crowds of people.
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