A finite incidence structure \({\mathcal J}\) is called a transversal translation design (TTD) if it admits (1.) a partition of the point set into classes such that (i) any two points of different classes are joined by a unique block; (ii) any two points of the same class are not joined by a block; (iii) each block meets each point class; and (2.) a point- regular group of automorphisms mapping each non-fixed block onto a disjoint block. Such a TTD may be described by means of a group partition \(S=\{T_ 0,T_ 1,...,T_ s\}\) of T (i.e. a set of subgroups \(T_ i\) of T with \(T_ i\cap T_ j=\{1\}\) for \(i\neq j)\) satisfying the condition \(T_ 0T_ i=T\) for each \(i\in \{1,...,s\}.\) The authors describe a method of constructing new group partitions of this type in the case of a Frobenius group. They use a so called H- admissible triad (K,\({\mathcal A},\Phi)\) with fixed point free automorphism group H. Such a triad consists of a group K, of a set \({\mathcal A}=\{K_ 0,K_ 1,...,K_ s\}\) of subgroups of K, of a bijective map \(\Phi\) between \(\{K_ 1,...,K_ s\}\) and \(K_ 0\) and of an automorphism group H of K such that the following conditions hold (with \(u_ i:=K_ i\Phi):\) (a) \(| K_ 0| =s\), \(| K_ i| =t\) for all \(i\in \{1,...,s\};\) (b) the elements of K which do not lie in any \(u_ i^{- 1}K_ iu_ i\) \((i=1,...,s)\) make a subgroup \(V_ 0\) of K; \((c)\quad \{V_ 0\}\cup \{u_ i^{-1}K_ iu_ i:\quad i=1,...,s\}\) is a group partition of K; \((d)\quad K=K_ 1u_ 1\cup K_ 2u_ 2\cup...\cup K_ su_ s;\) (e) each element of \({\mathcal A}\) is H-invariant. In the interesting case that K is not Abelian, such triads are constructed applying a method of \textit{A. Herzer} using alternative bisemilinear maps [Arch. Math. 34, 385-392 (1980; Zbl 0431.51001)]. The authors consider as well TTD's with orthogonal resolutions and give examples of \(T_ 0\)-regular transversal designs. To summarize, we can say that, with this interesting article, the authors continued the work on construction and classification of TTD's and made possible the characterization of TTD's given by the referee in Eur. J. Comb. (1985).