On the x0y plane let there be specified a complete metric of negative curvature K by means of the line element ds2=dx2+B2(x, y) dy2, and, in the strip Πa={0⩽x⩽a, ∞- 0,K⩽-μ2<0 (λ and μ are constants). Then, the metric in strip Πa is embedded in R3 by means of a surface of class C3.