Directional-correlation measurements were performed on the allowed 2.86-MeV β-0.845-MeV γ transition in the decay of Mn56. The results indicate that a small negative correlation (A2=-0.0030+/-0.0011) exists. For comparison, the β-γ directional correlation was also measured in the allowed β decay of I131. The distribution was found to be isotropic within the experimental error and the correlation coefficient was found to be |A2|<0.0005 in this case. The deviation of the Mn56 β spectrum from allowed shape is discussed and it is shown that a shape factor of the form C~1+0.04W-0.01W would not be inconsistent with the observed anisotropy.