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The track, entitled Speechless is available as a free download on the Monster Mondays website, which is run by her husband Swiss Beatz.
The song samples Devil In A New Dress by Kanye West and was produced by Swizz.
Speaking about the free giveaway on Twitter Alicia said: "Speechless is a little freestyle treat 4 the holidays. It's not a new album, not a single it's something special 4 U!
"My gift to you - a little song about my lil guy ;-) love to you - let's make 2011 incredible!!!"
Egypt was born in October.