Angry customers are calling out Bank of America after it tightened the rules for free checking.

The bank's eBanking accounts weren't technically free: An $8.95 monthly fee applied to customers who visited tellers for routine transactions. But clients who did their banking online didn't have to pay, no matter how low their balance got.

Now all customers with eBanking accounts have been moved to Core Checking, which carries a $12 monthly fee. Customers can avoid that fee if they make a monthly direct deposit of at least $250 or maintain a balance of $1,500. Students and customers in a rewards program are also exempt.

The bank introduced eBanking accounts in 2010 and stopped offering them in 2013. Bank of America (BAC) has been moving eBanking customers to Core Checking for years. The last group was notified in October and moved over on Friday.

Many customers weren't happy about it. A Change.org petition opposed to the new rules had more than 45,000 signatures on Monday.

"Bank of America was known to care for both their high income and low income customers. That is what made Bank of America different," wrote Mel San, who started the petition.

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Some people wrote that they cut ties with the bank over what they saw as unfair treatment of customers. One called it an unnecessary burden on the poor.

The petition launched January 5. About 17,000 signatures were added over the past week, and about 600 on Monday alone.

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Bank of America said through a spokeswoman that Core Checking is "a great value."

She stressed that it provides full access to banks, ATMs, mobile and online banking and offers several ways to avoid the monthly fee.

Other major banks offer similar services. Citi (C)'s Access account charges $10 a month, and customers can avoid the fee by making a qualifying direct deposit or bill payment per period, or keeping at least $1,500 in certain linked accounts.

And Chase (JPM) waives the $12 monthly fee on its Total Checking account for people who make direct deposits of at least $500 per month, maintain a minimum daily balance of $1,500 in the account or have at least $5,000 in qualifying linked deposits and investments.

Customers seeking a lower-cost option from Bank of America can sign up for the bank's SafeBalance account, which has a flat fee of $4.95 per month and doesn't allow overdrafts.