One way to modify gravity at small energy scale is to consider theories in which both vierbein and connection are dynamical fields. It has been known for long time that at certain values of parameters, linear perturbations about Minkowski background in these theories are free of instabilities (ghosts or tachyons), and yet contain massive spin-2 mode. We address the issue of whether the instabilities reappear in curved backgrounds. To this end, we introduce the cosmological constant and study perturbations about the general Einstein backgrounds. We find, somewhat surprisingly, that unlike in the case of the Fierz--Pauli massive gravity that suffers from the Boulware--Deser ghost instability, the model we discuss is healthy and no new propagating modes appear in the Einstein backgrounds, at least when the curvature of the background is sufficiently small. Another interesting property of the model is the existence of a self-accelerating solution at zero cosmological constant. Whether this solution is stable remains an open question.