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An X-ray cross-correlation study of the local orientational order in self-assembled films made from PEGylated gold nanoparticles is presented. The local structure of this model system is dominated by four- and sixfold order. Coadsorption of shorter ligands in the particle's ligand layer and variation of salt concentration in the suspension prior to self-assembly result in a change of local orientational order. The degree of sixfold order is reduced after salt addition. This decrease of order is less pronounced for the fourfold symmetry. The results presented here suggest complex symmetry-selective order formation upon ligand exchange and salt addition and demonstrate the versatility of X-ray cross-correlation methods for nanoparticle superlattices.