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We design, analyse and test a class of incomplete orthogonal factorization reconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations. Comphrehensive accounts about how the preconditioners are coded, what storage is required and how the computation is executed for a given accuracy is presented. A number of numerical experiments show that these preconditioners are competitive with standard incomplete triangular factorization preconditioners when they are applied to accelerate Krylov subspace iteration methods such as GMRES and BiCGSTAB.