Covariant scalar-tensor theories of gravity can be reformulated as spatially covariant gravity (SCG) theories in the unitary gauge. In the previous work , , an important ingredient --- time derivative of the lapse function --- was overlooked. Based on our recent paper , I will discuss how to build SCG theories with kinetic terms for both the spatial metric and the lapse function. Generally such kind of theories propagate 4 physical degrees of freedom, one of which is a ghost mode. Through a detailed Hamiltonian analysis, we derive two conditions that the Lagrangian must satisfy in order to get rid of this ghost mode. I will also discuss some simple examples as well as cosmological implications.