Formalised linguistic data integrated in Natural Language Processing tools can prove useful in enhancing learning of Modern Greek as a foreign/second language. Our research focuses on transitive non-locative constructions with a concrete direct object (CDO). For example: (a) Η νοσοκόµα κλείδωσε την πόρτα "The nurse locked the door". Our proposal focuses on learning CDO by means of Unitex, a corpus processing system based on automata oriented technology. For this purpose, we have elaborated a lexicon-grammar table that includes verbs used in simple sentences containing a CDO in Modern Greek. The lexicon-grammar is a syntactic model dedicated to description of elementary sentences of a natural language. The description is given in the form of a binary matrix. In our research, this means that a verb has or has not a given property. Moreover, we created a parameterised finite state automaton that constitutes the symbolic representation of a lexicon-grammar table, enriched by finite state automata that represent Greek noun phrases. By noun phrases we mean the noun (substantive, pronoun or any other nominal) as a head of the noun phrase, along with all its determiners and modifiers. For example: (b) Η νοσοκόµα κλείδωσε την πόρτα του δωµατίου του ασθενή (lit. The nurse locked the door of the room of the patient) "The nurse locked the patient’s room". We applied these linguistic resources on various authentic corpora (in different domains, such as science, economics, culture, etc.), in the context of Content and Language Integrated Learning (CLIL). We came up with a significant number of concordances of great utility, since they provide the possibility to study the use of a given construction in large-scale corpora. Therefore, they contribute to heuristic methods of teaching. The proposed method of CDO learning is recommended as a complement to learners at levels B2, C1, C2 of the Common European Framework of Reference for Languages (CEFR), set forth by the Council of Europe. Additionally, we have taken into account sample tests, past papers and guides to the examinations for the Certificate of Attainment in Modern Greek, organised by the Centre for the Greek Language.