In a manner quite similar to the Yang-Mills field strength which acquires additional two-dimensional σ-function terms under the singular gauge transformations, the Riemann-Christoffel curvature tensor in general relativity can also acquire such δ-function terms under a certain type of co-ordinate transformations on a certain class of space-times. As an illustration a Curzon metric with the conical-type singularities is adopted and the transformation properties of its energy-momentum tensor under singular co-ordinate transformations are discussed.