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We propose a simple heterodimer system consisting of a long and a short Au nanobar to achieve Fano-type resonances based on the destructive interference between the superradiant and subradiant modes without involvement of higher-order multipolar modes of individual components.The plasmonic modes are identified by the distributions of the electric field and charge density.By introducing another short nanobar on the other side of the long nanobar,the dipole moment of the system can be further cancelled and the spectral detuning between the superradiant and subradiant mode is decreased.As a result,the Fano-type resonance becomes deeper and its shape is more symmetric.This Fano-type resonance can be utilized in the refractive index sensing because of its narrow linewidth and steep dip.The figure of merit(FoM)can reach as high as 8.74,which is comparable with the results realized in more complicated systems involved with higher order modes.