We study a family of skew products FA,t = (σω, At)
over irrational rotation σω(x) = x + ω of a circle
T1, which depend on a real parameter t. It is supposed that the transformation At ∈ C(T1, SL(2,R))
is of the form At(x) = R(ϕ(x))Z(λ(x)), where R(ϕ)
stands for a rotation in R2 over an angle ϕ and
Z(λ) = diag{λ, λ−1} is a diagonal matrix. Assuming λ(x) ≥ λ0 1 and the function ϕ to be piecewise linear such that cos(x) possesses only simple
zeroes, we study the problem of uniform hyperbolicity for the cocycle generated by FA,t. We apply
the critical set method to formulate sufficient conditions on the parameter values which guarantee the
uniform hyperbolicity of the cocycle. Application to
the Schr¨odinger cocycles is also discussed.