We report the experimental observation of Kerr beam self-cleaning in a graded-index multimode fiber, leading to output beam profiles different from a bell shape, close to the $LP_{01}$ mode. For specific coupling conditions, nonlinear coupling among the guided modes can reshape the output speckle pattern generated by a pulsed beam into the low order $LP_{11}$ mode. This was observed in a few meters long multimode fiber with 750 ps pulses at 1064 nm in the normal dispersion regime. The power threshold for $LP_{11}$ mode self-cleaning was about three times larger than that required for Kerr nonlinear self- cleaning into the $LP_{01}$ mode.
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