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The hose instability of the drive beam constitutes a major challenge for the stable operation of plasma-wakefield accelerators. In this Letter, we show that drive beams with a transverse size comparable to the plasma blowout radius generate a wake with a varying focusing along the beam, which leads to a rapid detuning of the slice-betatron oscillations and suppresses the instability. This intrinsic stabilization principle provides an applicable and effective method for the suppression of the hosing of the drive beam and allows for a stable acceleration process.
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