Satellite measurements of the cosmic microwave back-ground radiation will soon provide an opportunity to test whether
the universe is multiply connected. This paper presents a new
algorithm for deducing the topology of the universe from the microwave background data. Unlike an older algorithm, the new
algorithm gives the curvature of space and the radius of the last
scattering surface as outputs, rather than requiring them as inputs. The new algorithm is also more tolerant of errors in the
observational data.