Computer monitor goes black

Hello,
help!my computer monitor goes black even if cpu is running and power is on .when i boot it, it goes well for few seconds and black screen appears again. i turn it off and turn on again i see no interruption to the running program but the problem persist.cables are properly connected.so i replace this with other monitor to check and it runs perfectly well no black screen appears.i return the 1st monitor and there goes the problem again!can you help solve this problem?thanks a lot