The Hilbert transform has been used to characterize wave propagation and detect phase singularities during cardiac fibrillation. Two mapping modalities have been used: optical mapping (used to map atria and ventricles) and contact electrode mapping (used only to map ventricles). Due to specific morphology of atrial electrograms, phase reconstruction of contact electrograms in the atria is challenging and has not been investigated in detail. Here, we explore the properties of Hilbert transform applied to unipolar epicardial electrograms and devise a method for robust phase reconstruction using the Hilbert transform. We applied the Hilbert transform to idealized unipolar signals obtained from analytical approach and to electrograms recorded in humans. We investigated effects of deflection morphology on instantaneous phase. Application of the Hilbert transform to unipolar electrograms demonstrated sensitivity of reconstructed phase to the type of deflection morphology (uni- or biphasic), the ratio of R and S waves and presence of the noise. In order to perform a robust phase reconstruction, we propose a signal transformation based on the recomposition of the electrogram from sinusoidal wavelets with amplitudes proportional to the negative slope of the electrogram. Application of the sinusoidal recomposition transformation prior to application of the Hilbert transform alleviates the effect of confounding features on reconstructed phase.