A Contract of Indemnity is a contractual obligation whereby one party (the indemnifier) promises to compensate the other party (the indemnity holder or indemnitee) for any loss or damage incurred. The primary characteristic of indemnity contracts is the protection against loss.

Let's analyze each option to determine which does not fit the classification of a Contract of Indemnity:

1. Contract of Fire Insurance: This is a contract whereby the insurer promises to indemnify the insured for any losses or damages due to fire during the contracted period. It clearly fits the definition of a Contract of Indemnity as it provides compensation for loss.
2. Contract of Marine Insurance: Similar to fire insurance, marine insurance covers losses or damages to maritime vessels and cargo. It also adheres to the principles of indemnity since it provides compensation for loss or damage.
3. Contract of Motor Insurance: This contract promises to compensate the policyholder for losses or damages involving a vehicle. Like the other two, it aligns with the concept of indemnity.
4. Contract of Life Insurance: This contract is an agreement where the insurer agrees to pay a predetermined sum upon the occurrence of a certain event, such as the insured’s death or after a set period. Importantly, it does not involve indemnifying specific losses incurred, thus not fitting the precise definition of a Contract of Indemnity.

Conclusion: Among the options, the "Contract of Life Insurance" is not a Contract of Indemnity. Life insurance pays the agreed sum upon an event like death, irrespective of any specific loss or damage incurred by the policyholder before that event.