Yes, but did you know there is "good" cholesterol as well as "bad" cholesterol, and when cholesterol is found in nature -- as in egg yolks -- both are found therein, as well as substances such as lecithin which help to break down the cholesterol.
LDL and HDL are lipoproteins which transport cholesterol. There is no "good" or "bad" cholesterol.
When you reduce your consumption of cholesterol, the liver makes up for some of that reduction with the production of endogenous cholesterol. In most cases, removing cholesterol entirely from your diet will only reduce your total cholesterol by 5% to 10%. In my case, it took my LDL from the low 300s mg/dl to the 190s. Everyone's liver behaves differently.