Veteran airline investor Bill Franke of Indigo Partners signed the preliminary order on Wednesday morning to buy 430 planes, comprising of 273 A320neos and 157 A321neos.
At current list prices, these additional aircraft are worth in excess of US$17.2 billion although discounts will be granted by Airbus.
The order by Indigo Partners trumps the 2015 order for 250 single-aisle planes valued at $27 billion by Indian budget carrier IndiGo.
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The order, believed to be the biggest ever for Airbus, will more than double the value of the airline's sales for the year.
Franke's Indigo Partners, which controls Denver-based Frontier Airlines and owns part of Mexico's Volaris, is known for unbundled or a la carte fares in so-called ultra-low-cost airlines, where passengers are offered cheap base prices with the option of paying more for extras.
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Airbus said the deal would be finalised before the end of this year.
The air show is proving a positive one for Airbus, who began the annual event lagging behind rival Boeing in the order department in 2017, so far.
Separately, Egyptair, which placed an initial order for 12 Bombardier CSeries on Tuesday, could return for more airplanes from the larger planemakers, industry sources said.
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In addition, a separate deal for 175 jets from flyDubai, possibly to be split between Airbus and Boeing is also on the cards.