is it normal to have "Non Competition" condition in job offer letter? the condition means that i should not have commit any business with their client (directly o indirectly) for 1 year duration following the date i quit from their company.

put it in this scenario:
H is a client for both Company E and Company M.
let's say i agree with this condition, take the job offer, then start working in company E and handle H's project. after few months, i have a another job offer from company M which also handle H's project.
i know this "Non Competition" condition definately have some impacts during career change. How deep will the impact be? Will company M just trun away because i am tied to this "non competition" condition?

any advice o opinion?