stalk of a leaflet.
Merriam-Webster Online Dictionarypetiolule
a stalk of a leaflet of a compound leaf
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In botany, the petiole () is the stalk that attaches the leaf blade to the stem. Outgrowths appearing on each side of the petiole in some species are called stipules. Leaves lacking a petiole are called sessile or epetiolate.