This paper will partly strengthen a recent application of model theory to the construction of sets of pairwise nonembeddable universal locally finite groups [8]. Our result is Theorem. There is a set U \mathcal {U} of 2 ℵ 1 {2^{{\aleph _1}}} universal locally finite groups of order ℵ 1 {\aleph _1} with the following properties: 0.1. If U ≠ V ∈ U U \ne V \in \mathcal {U} and A and B are uncountable sugroups of U and V, then A and B are not isomorphic. Let A be an uncountable subgroup of U ∈ U U \in \mathcal {U} . 0.2. A does not belong to any proper variety of groups, and 0.3. A is not isomorphic to any of its proper subgroups. 0.4. Every U ∈ U U \in \mathcal {U} is a complete group (every automorphism of U is inner).