Staggered solution procedures represent the most elementary computational strategy for the simulation of fluid–structure interaction problems. They usually consist of a predictor followed by the separate execution of each subdomain solver. Although it is generally possible to maintain the desired order of accuracy of the time integration, it is difficult to guarantee the stability of the overall computation. In the context of large solid over fluid mass ratios, compressible flows and explicit subsolvers, substantial development has been carried out by Felippa, Park, Farhat, Löhner and others. In this work, a new staggered scheme is presented. It is shown that, for a linear model problem, the scheme is second-order accurate and unconditionally stable. The dependency of the leading truncation error on the solid over fluid mass ratio is investigated. The strategy is applied to two-dimensional and three-dimensional fluid–structure interaction problems. It is shown that the conclusions derived from the investigation of the model problem apply. The new strategy extends the applicability of staggered schemes to problems involving relatively small solid over fluid mass ratios and incompressible fluid flow. It is suggested that the proposed scheme has the same range of applicability as the Dirichlet–Neumann or block Gauß–Seidel type strategies. Copyright © 2012 John Wiley & Sons, Ltd.