  We show that a critical condition exists in four dimensional scale invariant
gravity given by the pure quadratic action $\beta \,C_{\mu\nu\sigma\rho}
C^{\mu\nu\sigma \rho} + \alpha \,R^2$ where $C^{\mu}_{\,\,\nu \sigma \rho}$ is
the Weyl tensor, $R$ is the Ricci scalar and $\beta$ and $\alpha$ are
dimensionless parameters. The critical condition in a dS or AdS background is
$\beta =6 \alpha$. This leads to critical gravity where the massive spin two
physical ghost becomes a massless spin two graviton. In contrast to the
original work on critical gravity, no Einstein gravity with a cosmological
constant is added explicitly to the higher-derivative action. The critical
condition is obtained in two independent ways. In the first case, we show the
equivalence between the initial action and an action containing Einstein
gravity, a cosmological constant, a massless scalar field plus Weyl squared
gravity. The scale invariance is spontaneously broken. The linearized
Einstein-Weyl equations about a dS or AdS background yield the critical
condition $\beta=6\alpha$. In the second case, we work directly with the
original quadratic action. After a suitable field redefinition, where the
metric perturbation is traceless and transverse, we obtain linearized equations
about a dS or AdS background that yield the critical condition $\beta=
6\alpha$. As in the first case, we also obtain a propagating massless scalar
field. Substituting $\beta=6\alpha$ into the energy and entropy formula for the
Schwarzschild and Kerr AdS or dS black hole in higher-derivative gravity yields
zero, the same value obtained in the original work on critical gravity. We
discuss the role of boundary conditions in relaxing the $\beta=6\alpha$
condition.
