BAD : I thought that offering to help him might improve our relation.
GOOD : I thought that offering to help him might improve our relationship.
BAD : The relation between teachers and students is very friendly.
GOOD : The relationship between teachers and students is very friendly.
RELATION · RELATIONSHIP ·RELATIONS
Relation (1) the way in which one person or thing is connected with another: ‘We’ve been studying the relation between gender and income.’ ‘This latest murder bears no relation to the earlier killings.’
(2) someone who belongs to your family; relative: ‘She took me back home to meet all her friends and relations.’
Relationship the way that two people, groups or countries feel about each other and behave towards each other: ‘What kind of relationship did you have with your father?’ ‘Successful companies know the importance of establishing good relationships with their customers.’ ‘This decision will not affect the relationship between France and its European partners.’
Relations (plural noun) the way that two groups, countries or regions publicly or officially feel about and behave towards each other: ‘Relations between the two countries have steadily deteriorated in recent years.’ ‘The police are making great efforts to improve relations with the public.’
BAD : The new government is trying to improve its relation with America.
GOOD : The new government is trying to improve relations with America.
See Language Note above