This is a logically untenable position. One which Sartre labeled cowardly. You can only have morals without God if you water down the meaning of the word 'moral'. Even that will not pass muster though.
But, you sound quite certain. Tell me, all of us, what basis there is for morality if not from a transcendental force. If you can do it it will be a historic moment. Sartre failed and so have far greater minds than him. But go ahead, we're all ears.
Okay! I'll try, but don't forget to nominate me for a Nobel Prize.
When discussing such topics it's important to be very precise with the definitions of the key words involved. The word 'moral' is derived from the Latin, 'Moralis' which refers to the proper behaviour and manners of a person in society. The word is associated with concepts such as mores, customs and disposition.
The word 'transcendent', from the Latin 'transcendentum' refers to a process of 'surmounting, or rising above'. Extending the meaning, we get 'surpassing the usual limits beyond the range of usual perception', and 'free from the constraints of the material world'.
I'm guessing that the last phrase, 'free from the constraints of the material world' is what you have in mind when you refer to a 'transcendental force'.
So, to address your question, 'what basis is there for a morality which is not from a transcendental force', I offer the following argument.
The evolutionary process of all creatures on the planet, relies upon a morality (or proper behaviour) which is appropriate for the circumstance and the environment.
An ant hill, as in the attached image, which is a complex city of tunnels in a mound of earth, cannot be built and maintained without the ants conforming to a strict sense of proper behaviour, or morality. You might call it 'ant-like morality', or 'instinct-driven morality', but it is nevertheless a type of morality which is essential for the ants' survival in their present situation.
When the environment changes, for whatever reason, meteorite strikes, volcanic eruptions, earthquakes, changes in the earth's orbit, and so on, those creatures that fail to adapt to the changing conditions tend to become extinct. Those than can and do adapt, survive.
We exist because of the adaptive skills of our ancestors. Adaptive skills in creatures with small brains, like ants, are more dependent on genetic mutations and genetic variability.
Big-brained creatures like Homo Sapiens, who are now able to communicate almost instantaneously across the world, for the first time in the history of our planet, have a tremendous capacity to adapt to any changing environmental conditions.
When we fail to adapt, which is sometimes (perhaps often) the case, we have the capacity to learn from history (or at least some of us do).
The paleontological record of our early ancestors suggests that Neanderthal man (or Homo Sapiens Neanderthalensis) became extinct due to his inability to adapt to the encroaching Ice Age. The last 'Glacial Maximum' occurred about 24,500 BC. The cooling period began about 110,00 years ago. Neanderthal man became extinct about 40,000 years ago. The climate was getting colder and colder during those thousands of years, with many decades of alternating ups and downs, no doubt as we observe today.
Homo Sapiens Sapiens (as distinct from Homo Sapiens, who was also Neanderthal man) was able to adapt to those terribly cold conditions. The very low sea levels also helped the migration of tribes from Africa who were able to walk across areas that are now covered by sea. No boats were required.
The early Aboriginal settlers in Australia were also able walk into Australia and Tasmania, because sea levels were so low.
When discussing morality with religious connotations, we should not forget that many religious moral principles were first initiated as purely practical measures to counteract or prevent observed harmful effects. Eating diseased pigs, several centuries ago, was observed by the more intelligent members of the community, to be harmful to health. Banning the eating of pork can therefore be viewed as a rational decision by those in power at the time.
Unfortunately, religions in general tend to set dogmatic rules which might once have served a practical purpose, but might not serve any useful purpose in the changed conditions of a modern society. That's the tragedy of religious belief.
I like to use images to illustrate my point, so I've included a second photo of a lovely 'Long Neck' lady from Northern Thailand. Aren't the rings around her neck lovely! All females from an early age are required to permanently wear such rings in this society. Why? Why? Why? Is it purely decorative?
According to the Museum of Hill Tribe People in that area, there was a sound practical reason for women to wear such rings. Centuries ago, the job of the woman was to work in the fields harvesting crops. Tigers were a major predator in those days and would tend to attack the women by going for the jugular.
Some smart and adaptive chieftain sought a practical solution. All women must protect their jugular. The practice continues even though the original purpose no longer applies.
I rest my case.