Let $(y_{1i},y_{2i}),i=1,\dots ,N$, have a bivariate normal distribution with mean $({\mu }_1,{\mu }_2)$ and covariance parameters $({\sigma }_{11},{\sigma }_{12},{\sigma }_{22})$ and correlation coefficient $\rho$. Suppose that all $N$ observations on $y_1$ are available but there are $m<N$ missing observations on $y_2$. Using the fact that the marginal distribution of $y_j$ is $\mathcal{N}[{\mu }_j,{\sigma }_{jj}]$, and that conditionally $y_2\mid y_1\sim \mathcal{N}[{\mu }_{2.1},{\sigma }_{22.1}]$, where ${\mu }_{2.1}={\mu }_2+$ ${\sigma }_{12}/{\sigma }_{22}(y_1-{\mu }_1),{\sigma }_{22.1}=(1-{\rho }^2){\sigma }_{22}$, devise an EM algorithm for imputing the missing observations on $y_1$.