The invention relates to a method for the selective recovery of at least one rare earth present in a waste, which comprises the following steps: (a) dissolving the waste in divided form in an acidic aqueous solution to release the rare earth in the liquid phase, (b) collection of the liquid phase, (c) precipitation of the rare earth in the form of a double sulfate of rare earth by introduction of a sulfate into the liquid phase collected at the end of the step (b), and (d) collection of the precipitate. Step (a) of dissolution is carried out by immersion and maintenance, for a time t, of the waste in divided form in an aqueous solution S1 comprising hydrochloric acid and having a constant pH and equal to a value between 1, 5 and 4.5 during time t. The invention also relates to a process for recovering a waste comprising at least one rare earth implementing this recovery process.
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