The business is shared by JWT, McCann Erickson and Euro RSCG.
The networks have all been asked to produce a television spot for one of three of the company's brands: Clearasil, which is currently run by McCann; Veet, which is handled by JWT; and Air Wick, which is held by Euro RSCG.
McCann is the latest addition to the Reckitt roster. It joined earlier this year following Reckitt's £1.9bn acquisition of Boots Healthcare International.
The deal saw Reckitt, which owns brands such as Lemsip, Dettol, Gaviscon and Finish, also acquire the Clearasil, Strepsils, Nurofen, Optrex and E45 brands.
Reckitt then moved its £14m UK media planning and buying into OMD, its existing agency, without a pitch.
It was thought Euro RSCG and JWT would share BHI's creative account. However, it retained McCann, which had held the business since 1997.
JWT and Euro RSCG picked up the Reckitt account in 2002 after a three-way pitch that also included Ogilvy & Mather. McCann was the incumbent, but resigned the business after its Interpublic parent bought True North, which handled SC Johnson.
In July, Reckitt signed a £10m sponsor deal for ITV's Emmerdale, covering ITV1, ITV2, ITV3 and online.
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