  The 'tHooft's 5N-parametric multiinstanton solution is generalized to
curvilinear coordinates. Expressions can be simplified by a gauge
transformation that makes $\eta$-symbols constant in the vierbein formalism.
This generates the compensating addition to the gauge potential of
pseudoparticles. Typical examples (4-spherical, 2+2- and 3+1-cylindrical
coordinates) are studied and explicit formulae presented for reference.
Singularities of the compensating field are discussed. They are irrelevant for
physics but affect gauge dependent quantities.
