  We consider a twin Higgs scenario where the $Z_2$ twin symmetry is broken
spontaneously, not explicitly. This scenario provides an interesting
interpretation of the Higgs metastability in the standard model; the $SU(4)$
breaking scale $f$ is determined by the scale where the Higgs self quartic
coupling flips its sign. However, for the misalignment of nonzero vacuum
expectation values of the twin Higgs fields, parameter tuning of ${\cal
O}(m_h^2/f^2)$ is required like explicit twin symmetry breaking scenarios. For
the minimal model with the exact twin symmetry, $f$ is ${\cal O}$($10^{10}$
GeV), so the model is very unnatural. We point out that the tuning can be
significantly reduced ($f\gtrsim 2.7$ TeV) if there are twin vector-like
leptons with large Yukawa coupling to twin Higgs fields.
