In this paper we provide an extension of special parametric class of perturbations of an arbitrary copula (given in [3]) that represent a partial generalization of the FGM family of copulas for parameters from the unit interval. However the FGM family is defined for parameters from the interval [-1,1]. We present a construction of perturbations of an arbitrary copula also for parameters from the interval [-1,0] so that together with the former family of perturbations of copulas we get a generalization of the FGM family for the whole interval [-1,1]. We also investigated the influence of the parameters of the introduced class of perturbations of copulas on several measures of dependence (Spearman's rho, Blomqvist's beta, Gini's gamma, Kendall's tau).
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