  We propose a new class of higher derivative scalar-tensor theories without
the Ostrogradsky's ghost instabilities. The construction of our theory is
originally motivated by a scalar field with spacelike gradient, which enables
us to fix a gauge in which the scalar field appears to be non-dynamical. We dub
such a gauge as the spatial gauge. Though the scalar field loses its dynamics,
the spatial gauge fixing breaks the time diffeomorphism invariance and thus
excites a scalar mode in the gravity sector. We generalize this idea and
construct a general class of scalar-tensor theories through a non-dynamical
scalar field, which preserves only spatial covariance. We perform a Hamiltonian
analysis and confirm that there are at most three (two tensors and one scalar)
dynamical degrees of freedom, which ensures the absence of a degree of freedom
due to higher derivatives. Our construction opens a new branch of scalar-tensor
theories with higher derivatives.
