Log4j - Issue with DailyRollingFileAppender

We are using log4j for logging and we have an issue.

Below is the log4j config file .We are using DailyRollingFileAppender to rotate logs daily.

configure the root logger

log4j.rootLogger=DEBUG, DAILY

configure the daily rolling file appender

log4j.appender.DAILY.DatePattern=’.’ yyyy-MM-dd
log4j.appender.DAILY.layout.conversionPattern=%d{yyyy-MM-dd HH:mm:ss.SSS} ^ [%p] ^ %c ^%m%n

The issue is that for each day it rolls over to a new log file and logs are being written there.
But few logs are being written to the old existing log file as well from the previous day.
Has anyone experienced this issue.
Please suggest how to fix this.