"I have a problem of the greatest importance to the company."

"I have news of the greatest importance for your ears alone."

Not important to you now, but of the greatest importance one day.

Certainly it is an issue of the greatest public importance.

Perhaps not of the greatest importance, but something which must be accomplished.

Our answer to this question is of the greatest importance.

On no account must they part until something of the very greatest importance had happened.

In the 14th century the family got the greatest importance.

Therefore, you could in a sense say that this was not a matter of the very greatest importance.

We are talking about a matter of the greatest importance.