We present a novel relaxed maximum likelihood solution to the problem of direct localization of multiple narrowband  sources by partly calibrated arrays, i.e., arrays composed of  fully calibrated subarrays yet lacking  inter-array calibration. The proposed solution is based on eliminating analytically all the nuisance parameters in the problem, thus reducing the likelihood function to a maximization problem involving only the location of the sources.  The performance of the solution is demonstrated via simulations.