While performing a task as instructed by your supervisor, you discover what seems to be a better way of doing the work. You should:

Continue to perform the task as instructed: It's important to complete the task as per the instructions given by your supervisor. This ensures that the work is done in a way that is consistent with the company's standards and procedures.

Document your new method: Write down the steps of your new method, detailing how it differs from the current method and why you believe it is better. This could include things like it being more efficient, cost-effective, or producing higher quality results.

Test your method: If possible, test your new method to ensure it works as expected. This could involve doing a small-scale trial or simulation.

Present your findings to your supervisor: Once you have all your information and results, arrange a meeting with your supervisor. Present your new method, along with your reasons for believing it is better and any results from your testing. Be sure to communicate clearly and respectfully, acknowledging the current method while explaining the potential benefits of your proposed change.

Accept feedback: Be open to feedback from your supervisor. They may have insights or considerations that you hadn't thought of. If they approve of your new method, great! If not, accept their decision gracefully and continue to perform your tasks as instructed.