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McLaren Rulez

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I am using Griener's Relativistic Quantum Mechanics and I have a question. Using the Klien Gordon Equation [itex](p^{\mu}p_{\mu}-m_{0}c^{2})\psi=0[/itex], he says that the transformation law for the wavefunction i.e [itex]\psi(x)[/itex] transforming to [itex]\psi'(x')[/itex] must have the form [itex] \psi'(x')=\lambda \psi(x)[/itex] with [itex]|\lambda|=1[/itex]. I don't understand why this is the case. Can anyone help me see why this must be so?

Thank you