  We describe Morita equivalence of unital locally matrix algebras in terms of
their Steinitz parametrization. Two countable dimensional unital locally matrix
algebras are Morita equivalent if and only if their Steinitz numbers are
rationally connected. For an arbitrary uncountable dimension $\alpha$ and an
arbitrary not locally finite Steinitz number $s$ there exist unital locally
matrix algebras $A$, $B$ such that $\dim_{F}A=\dim_{F}B=\alpha$,
$\mathbf{st}(A)=\mathbf{st}(B)=s$, however, the algebras $A$, $B$ are not
Morita equivalent.
