  Context. Very Long Baseline Interferometry (VLBI) data are extremely
sensitive to the phase stability of the VLBI array. This is especially
important when we reach {\mu}Jy r.m.s. sensitivities. Calibration using
standard phase referencing techniques is often used to improve the phase
stability of VLBI data but the results are often not optimal. This is evident
in blank fields that do not have in-beam calibrators. Aims. We present a
calibration algorithm termed Multi-Source Self-Calibration (MSSC) which can be
used after standard phase referencing on wide-field VLBI observations. This is
tested on a 1.6 GHz wide-field VLBI data set of the Hubble Deep Field-North and
the Hubble Flanking Fields. Methods. MSSC uses multiple target sources detected
in the field via standard phase referencing techniques and modifies the
visibili- ties so that each data set approximates to a point source. These are
combined to increase the signal to noise and permit self-calibration. In
principle, this should allow residual phase changes caused by the troposphere
and ionosphere to be corrected. By means of faceting, the technique can also be
used for direction dependent calibration. Results. Phase corrections, derived
using MSSC, were applied to a wide-field VLBI data set of the HDF-N comprising
of 699 phase centres. MSSC was found to perform considerably better than
standard phase referencing and single source self-calibration. All detected
sources exhibited dramatic improvements in dynamic range. Using MSSC, one
source reached the detection threshold taking the total detected sources to
twenty. 60% of these sources can now be imaged with uniform weighting compared
to just 45% with standard phase referencing. The Parseltongue code which
implements MSSC has been released and made publicly available to the
astronomical community (https://github.com/jradcliffe5/multi_self_cal).
