Unable to delete a custom field from a contact

Greetings, I would like to ask you about the following:
How can I delete a custom field from a contact? When I try to edit the contact and delete the field (remove field from this contact) and then press save, it is still there in the contact. It seems that it is not saved.
Plese note that the contact from which I want to remove the field has been created using a smart form that included this speciffic field. But later I edited this form and now I wnat to remove this field from all the contacts that have it.